searching the database
Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St001688
(load all 10 compositions to match this statistic)
(load all 10 compositions to match this statistic)
St001688: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> 1
[1,0,1,0]
=> 2
[1,1,0,0]
=> 4
[1,0,1,0,1,0]
=> 3
[1,0,1,1,0,0]
=> 5
[1,1,0,0,1,0]
=> 5
[1,1,0,1,0,0]
=> 8
[1,1,1,0,0,0]
=> 9
[1,0,1,0,1,0,1,0]
=> 4
[1,0,1,0,1,1,0,0]
=> 6
[1,0,1,1,0,0,1,0]
=> 6
[1,0,1,1,0,1,0,0]
=> 9
[1,0,1,1,1,0,0,0]
=> 10
[1,1,0,0,1,0,1,0]
=> 6
[1,1,0,0,1,1,0,0]
=> 8
[1,1,0,1,0,0,1,0]
=> 9
[1,1,0,1,0,1,0,0]
=> 12
[1,1,0,1,1,0,0,0]
=> 13
[1,1,1,0,0,0,1,0]
=> 10
[1,1,1,0,0,1,0,0]
=> 13
[1,1,1,0,1,0,0,0]
=> 18
[1,1,1,1,0,0,0,0]
=> 16
[1,0,1,0,1,0,1,0,1,0]
=> 5
[1,0,1,0,1,0,1,1,0,0]
=> 7
[1,0,1,0,1,1,0,0,1,0]
=> 7
[1,0,1,0,1,1,0,1,0,0]
=> 10
[1,0,1,0,1,1,1,0,0,0]
=> 11
[1,0,1,1,0,0,1,0,1,0]
=> 7
[1,0,1,1,0,0,1,1,0,0]
=> 9
[1,0,1,1,0,1,0,0,1,0]
=> 10
[1,0,1,1,0,1,0,1,0,0]
=> 13
[1,0,1,1,0,1,1,0,0,0]
=> 14
[1,0,1,1,1,0,0,0,1,0]
=> 11
[1,0,1,1,1,0,0,1,0,0]
=> 14
[1,0,1,1,1,0,1,0,0,0]
=> 19
[1,0,1,1,1,1,0,0,0,0]
=> 17
[1,1,0,0,1,0,1,0,1,0]
=> 7
[1,1,0,0,1,0,1,1,0,0]
=> 9
[1,1,0,0,1,1,0,0,1,0]
=> 9
[1,1,0,0,1,1,0,1,0,0]
=> 12
[1,1,0,0,1,1,1,0,0,0]
=> 13
[1,1,0,1,0,0,1,0,1,0]
=> 10
[1,1,0,1,0,0,1,1,0,0]
=> 12
[1,1,0,1,0,1,0,0,1,0]
=> 13
[1,1,0,1,0,1,0,1,0,0]
=> 16
[1,1,0,1,0,1,1,0,0,0]
=> 17
[1,1,0,1,1,0,0,0,1,0]
=> 14
[1,1,0,1,1,0,0,1,0,0]
=> 17
[1,1,0,1,1,0,1,0,0,0]
=> 22
[1,1,0,1,1,1,0,0,0,0]
=> 20
Description
The sum of the squares of the heights of the peaks of a Dyck path.
Matching statistic: St001127
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00186: Skew partitions —dominating partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001127: Integer partitions ⟶ ℤResult quality: 64% ●values known / values provided: 64%●distinct values known / distinct values provided: 89%
Mp00186: Skew partitions —dominating partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001127: Integer partitions ⟶ ℤResult quality: 64% ●values known / values provided: 64%●distinct values known / distinct values provided: 89%
Values
[1,0]
=> [[1],[]]
=> [1]
=> [1]
=> 1
[1,0,1,0]
=> [[1,1],[]]
=> [1,1]
=> [2]
=> 4
[1,1,0,0]
=> [[2],[]]
=> [2]
=> [1,1]
=> 2
[1,0,1,0,1,0]
=> [[1,1,1],[]]
=> [1,1,1]
=> [3]
=> 9
[1,0,1,1,0,0]
=> [[2,1],[]]
=> [2,1]
=> [2,1]
=> 5
[1,1,0,0,1,0]
=> [[2,2],[1]]
=> [2,1]
=> [2,1]
=> 5
[1,1,0,1,0,0]
=> [[3],[]]
=> [3]
=> [1,1,1]
=> 3
[1,1,1,0,0,0]
=> [[2,2],[]]
=> [2,2]
=> [2,2]
=> 8
[1,0,1,0,1,0,1,0]
=> [[1,1,1,1],[]]
=> [1,1,1,1]
=> [4]
=> 16
[1,0,1,0,1,1,0,0]
=> [[2,1,1],[]]
=> [2,1,1]
=> [3,1]
=> 10
[1,0,1,1,0,0,1,0]
=> [[2,2,1],[1]]
=> [2,2]
=> [2,2]
=> 8
[1,0,1,1,0,1,0,0]
=> [[3,1],[]]
=> [3,1]
=> [2,1,1]
=> 6
[1,0,1,1,1,0,0,0]
=> [[2,2,1],[]]
=> [2,2,1]
=> [3,2]
=> 13
[1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> [2,1,1]
=> [3,1]
=> 10
[1,1,0,0,1,1,0,0]
=> [[3,2],[1]]
=> [3,1]
=> [2,1,1]
=> 6
[1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> [3,1]
=> [2,1,1]
=> 6
[1,1,0,1,0,1,0,0]
=> [[4],[]]
=> [4]
=> [1,1,1,1]
=> 4
[1,1,0,1,1,0,0,0]
=> [[3,3],[1]]
=> [3,2]
=> [2,2,1]
=> 9
[1,1,1,0,0,0,1,0]
=> [[2,2,2],[1]]
=> [2,2,1]
=> [3,2]
=> 13
[1,1,1,0,0,1,0,0]
=> [[3,2],[]]
=> [3,2]
=> [2,2,1]
=> 9
[1,1,1,0,1,0,0,0]
=> [[2,2,2],[]]
=> [2,2,2]
=> [3,3]
=> 18
[1,1,1,1,0,0,0,0]
=> [[3,3],[]]
=> [3,3]
=> [2,2,2]
=> 12
[1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1],[]]
=> [1,1,1,1,1]
=> [5]
=> 25
[1,0,1,0,1,0,1,1,0,0]
=> [[2,1,1,1],[]]
=> [2,1,1,1]
=> [4,1]
=> 17
[1,0,1,0,1,1,0,0,1,0]
=> [[2,2,1,1],[1]]
=> [2,2,1]
=> [3,2]
=> 13
[1,0,1,0,1,1,0,1,0,0]
=> [[3,1,1],[]]
=> [3,1,1]
=> [3,1,1]
=> 11
[1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1],[]]
=> [2,2,1,1]
=> [4,2]
=> 20
[1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1],[1,1]]
=> [2,2,1]
=> [3,2]
=> 13
[1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> [3,2]
=> [2,2,1]
=> 9
[1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1],[2]]
=> [3,2]
=> [2,2,1]
=> 9
[1,0,1,1,0,1,0,1,0,0]
=> [[4,1],[]]
=> [4,1]
=> [2,1,1,1]
=> 7
[1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1],[1]]
=> [3,3]
=> [2,2,2]
=> 12
[1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1],[1]]
=> [2,2,2]
=> [3,3]
=> 18
[1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1],[]]
=> [3,2,1]
=> [3,2,1]
=> 14
[1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1],[]]
=> [2,2,2,1]
=> [4,3]
=> 25
[1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1],[]]
=> [3,3,1]
=> [3,2,2]
=> 17
[1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2],[1,1,1]]
=> [2,1,1,1]
=> [4,1]
=> 17
[1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2],[1,1]]
=> [3,1,1]
=> [3,1,1]
=> 11
[1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> [3,2]
=> [2,2,1]
=> 9
[1,1,0,0,1,1,0,1,0,0]
=> [[4,2],[1]]
=> [4,1]
=> [2,1,1,1]
=> 7
[1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> [3,2,1]
=> [3,2,1]
=> 14
[1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3],[2,2]]
=> [3,1,1]
=> [3,1,1]
=> 11
[1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> [4,1]
=> [2,1,1,1]
=> 7
[1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [4,1]
=> [2,1,1,1]
=> 7
[1,1,0,1,0,1,0,1,0,0]
=> [[5],[]]
=> [5]
=> [1,1,1,1,1]
=> 5
[1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [4,2]
=> [2,2,1,1]
=> 10
[1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [3,2,1]
=> [3,2,1]
=> 14
[1,1,0,1,1,0,0,1,0,0]
=> [[4,3],[1]]
=> [4,2]
=> [2,2,1,1]
=> 10
[1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [3,2,2]
=> [3,3,1]
=> 19
[1,1,0,1,1,1,0,0,0,0]
=> [[4,4],[1]]
=> [4,3]
=> [2,2,2,1]
=> 13
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1,1,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1,1,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1,1],[1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
=> [[4,4,1,1],[2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1,1],[2,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3,1,1],[1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [[4,4,1,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2,1,1],[1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1,1],[2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=> [[2,2,2,2,1,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3,1,1],[2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [[3,3,3,1,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3,1,1],[]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=> [[3,3,2,2,1],[1,1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2,1],[2,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2,1],[2,1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2,1],[1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [[3,3,3,2,1],[1,1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [[4,4,2,1],[1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
=> [[4,4,3,1],[2,2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
=> [[5,5,1],[3]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=> [[4,4,4,1],[3,2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [[5,4,1],[2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> [[4,4,4,1],[2,2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [[5,5,1],[2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
=> [[3,3,3,3,1],[2,2,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3,1],[2,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3,1],[3,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=> [[5,3,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3,1],[2,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=> [[3,3,3,3,1],[2,1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=> [[4,3,3,1],[1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=> [[3,3,3,3,1],[1,1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [[4,4,3,1],[1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=> [[4,4,4,1],[3,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=> [[5,4,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [[4,4,4,1],[2,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [[5,5,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,2,1],[1,1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
=> [[3,2,2,2,1],[1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> [[3,3,2,2,1],[2,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
=> [[4,2,2,1],[1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2,1],[1,1]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
=> [[3,3,3,2,1],[2,2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
=> [[4,3,2,1],[2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=> [[4,4,2,1],[3]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=> [[4,4,2,1],[2]]
=> ?
=> ?
=> ? ∊ {14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,28,28,28,28,28,28,28,29,29,29,29,29,29,29,29,29,29,30,30,30,30,30,30,32,33,33,33,33,34,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,36,36,37,37,38,38,38,40,40,40,41,41,41,41,41,41,41,42,42,42,43,43,43,43,43,43,45,45,45,45,49,49,50,50,50,50,52,52,52,57,57,57,57,57,59,59,61,61,64,66,66,75}
Description
The sum of the squares of the parts of a partition.
Matching statistic: St001879
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 21%
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 21%
Values
[1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> ([(0,1)],2)
=> ? = 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> ([(0,2),(2,1)],3)
=> 2
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> ([(1,2)],3)
=> ? = 4
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {5,5,8,9}
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {5,5,8,9}
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3)],4)
=> ? ∊ {5,5,8,9}
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> ([(2,3)],4)
=> ? ∊ {5,5,8,9}
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(3,4)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(2,4)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(1,4)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ([(1,4),(2,3),(2,4)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> ([(3,4)],5)
=> ? ∊ {6,6,8,9,9,10,10,12,13,13,16,18}
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 7
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 7
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> ([(0,5),(4,3),(5,1),(5,2),(5,4)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> ([(0,5),(1,2),(1,3),(1,4),(4,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> ([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> ([(1,5),(2,5),(3,4),(3,5)],6)
=> ? ∊ {7,9,9,9,10,10,10,11,11,11,12,13,13,13,13,14,14,14,14,16,17,17,17,17,17,18,19,19,20,20,22,22,25,25,25,27,32}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> 8
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> 8
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> 8
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=> ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> 13
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
=> 8
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
=> 11
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 8
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)
=> 13
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0,1,0]
=> ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
=> 13
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> 12
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
=> 14
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> 20
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!