Identifier
-
Mp00044:
Integer partitions
—conjugate⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000108: Integer partitions ⟶ ℤ
Values
[1] => [1] => [] => 1
[2] => [1,1] => [1] => 2
[1,1] => [2] => [] => 1
[3] => [1,1,1] => [1,1] => 3
[2,1] => [2,1] => [1] => 2
[1,1,1] => [3] => [] => 1
[4] => [1,1,1,1] => [1,1,1] => 4
[3,1] => [2,1,1] => [1,1] => 3
[2,2] => [2,2] => [2] => 3
[2,1,1] => [3,1] => [1] => 2
[1,1,1,1] => [4] => [] => 1
[5] => [1,1,1,1,1] => [1,1,1,1] => 5
[4,1] => [2,1,1,1] => [1,1,1] => 4
[3,2] => [2,2,1] => [2,1] => 5
[3,1,1] => [3,1,1] => [1,1] => 3
[2,2,1] => [3,2] => [2] => 3
[2,1,1,1] => [4,1] => [1] => 2
[1,1,1,1,1] => [5] => [] => 1
[6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,1] => [2,1,1,1,1] => [1,1,1,1] => 5
[4,2] => [2,2,1,1] => [2,1,1] => 7
[4,1,1] => [3,1,1,1] => [1,1,1] => 4
[3,3] => [2,2,2] => [2,2] => 6
[3,2,1] => [3,2,1] => [2,1] => 5
[3,1,1,1] => [4,1,1] => [1,1] => 3
[2,2,2] => [3,3] => [3] => 4
[2,2,1,1] => [4,2] => [2] => 3
[2,1,1,1,1] => [5,1] => [1] => 2
[1,1,1,1,1,1] => [6] => [] => 1
[7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,2] => [2,2,1,1,1] => [2,1,1,1] => 9
[5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 5
[4,3] => [2,2,2,1] => [2,2,1] => 9
[4,2,1] => [3,2,1,1] => [2,1,1] => 7
[4,1,1,1] => [4,1,1,1] => [1,1,1] => 4
[3,3,1] => [3,2,2] => [2,2] => 6
[3,2,2] => [3,3,1] => [3,1] => 7
[3,2,1,1] => [4,2,1] => [2,1] => 5
[3,1,1,1,1] => [5,1,1] => [1,1] => 3
[2,2,2,1] => [4,3] => [3] => 4
[2,2,1,1,1] => [5,2] => [2] => 3
[2,1,1,1,1,1] => [6,1] => [1] => 2
[1,1,1,1,1,1,1] => [7] => [] => 1
[8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
[7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 11
[6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,3] => [2,2,2,1,1] => [2,2,1,1] => 12
[5,2,1] => [3,2,1,1,1] => [2,1,1,1] => 9
[5,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 5
[4,4] => [2,2,2,2] => [2,2,2] => 10
[4,3,1] => [3,2,2,1] => [2,2,1] => 9
[4,2,2] => [3,3,1,1] => [3,1,1] => 10
[4,2,1,1] => [4,2,1,1] => [2,1,1] => 7
[4,1,1,1,1] => [5,1,1,1] => [1,1,1] => 4
[3,3,2] => [3,3,2] => [3,2] => 9
[3,3,1,1] => [4,2,2] => [2,2] => 6
[3,2,2,1] => [4,3,1] => [3,1] => 7
[3,2,1,1,1] => [5,2,1] => [2,1] => 5
[3,1,1,1,1,1] => [6,1,1] => [1,1] => 3
[2,2,2,2] => [4,4] => [4] => 5
[2,2,2,1,1] => [5,3] => [3] => 4
[2,2,1,1,1,1] => [6,2] => [2] => 3
[2,1,1,1,1,1,1] => [7,1] => [1] => 2
[1,1,1,1,1,1,1,1] => [8] => [] => 1
[9] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 9
[8,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
[7,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 13
[7,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => 15
[6,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 11
[6,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,4] => [2,2,2,2,1] => [2,2,2,1] => 14
[5,3,1] => [3,2,2,1,1] => [2,2,1,1] => 12
[5,2,2] => [3,3,1,1,1] => [3,1,1,1] => 13
[5,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => 9
[5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 5
[4,4,1] => [3,2,2,2] => [2,2,2] => 10
[4,3,2] => [3,3,2,1] => [3,2,1] => 14
[4,3,1,1] => [4,2,2,1] => [2,2,1] => 9
[4,2,2,1] => [4,3,1,1] => [3,1,1] => 10
[4,2,1,1,1] => [5,2,1,1] => [2,1,1] => 7
[4,1,1,1,1,1] => [6,1,1,1] => [1,1,1] => 4
[3,3,3] => [3,3,3] => [3,3] => 10
[3,3,2,1] => [4,3,2] => [3,2] => 9
[3,3,1,1,1] => [5,2,2] => [2,2] => 6
[3,2,2,2] => [4,4,1] => [4,1] => 9
[3,2,2,1,1] => [5,3,1] => [3,1] => 7
[3,2,1,1,1,1] => [6,2,1] => [2,1] => 5
[3,1,1,1,1,1,1] => [7,1,1] => [1,1] => 3
[2,2,2,2,1] => [5,4] => [4] => 5
[2,2,2,1,1,1] => [6,3] => [3] => 4
[2,2,1,1,1,1,1] => [7,2] => [2] => 3
[2,1,1,1,1,1,1,1] => [8,1] => [1] => 2
[1,1,1,1,1,1,1,1,1] => [9] => [] => 1
[10] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 10
[9,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 9
[8,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 15
[8,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
[7,3] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 18
>>> Load all 863 entries. <<<[7,2,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 13
[7,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => 18
[6,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 15
[6,2,2] => [3,3,1,1,1,1] => [3,1,1,1,1] => 16
[6,2,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 11
[6,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,5] => [2,2,2,2,2] => [2,2,2,2] => 15
[5,4,1] => [3,2,2,2,1] => [2,2,2,1] => 14
[5,3,2] => [3,3,2,1,1] => [3,2,1,1] => 19
[5,3,1,1] => [4,2,2,1,1] => [2,2,1,1] => 12
[5,2,2,1] => [4,3,1,1,1] => [3,1,1,1] => 13
[5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 9
[5,1,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 5
[4,4,2] => [3,3,2,2] => [3,2,2] => 16
[4,4,1,1] => [4,2,2,2] => [2,2,2] => 10
[4,3,3] => [3,3,3,1] => [3,3,1] => 16
[4,3,2,1] => [4,3,2,1] => [3,2,1] => 14
[4,3,1,1,1] => [5,2,2,1] => [2,2,1] => 9
[4,2,2,2] => [4,4,1,1] => [4,1,1] => 13
[4,2,2,1,1] => [5,3,1,1] => [3,1,1] => 10
[4,2,1,1,1,1] => [6,2,1,1] => [2,1,1] => 7
[4,1,1,1,1,1,1] => [7,1,1,1] => [1,1,1] => 4
[3,3,3,1] => [4,3,3] => [3,3] => 10
[3,3,2,2] => [4,4,2] => [4,2] => 12
[3,3,2,1,1] => [5,3,2] => [3,2] => 9
[3,3,1,1,1,1] => [6,2,2] => [2,2] => 6
[3,2,2,2,1] => [5,4,1] => [4,1] => 9
[3,2,2,1,1,1] => [6,3,1] => [3,1] => 7
[3,2,1,1,1,1,1] => [7,2,1] => [2,1] => 5
[3,1,1,1,1,1,1,1] => [8,1,1] => [1,1] => 3
[2,2,2,2,2] => [5,5] => [5] => 6
[2,2,2,2,1,1] => [6,4] => [4] => 5
[2,2,2,1,1,1,1] => [7,3] => [3] => 4
[2,2,1,1,1,1,1,1] => [8,2] => [2] => 3
[2,1,1,1,1,1,1,1,1] => [9,1] => [1] => 2
[1,1,1,1,1,1,1,1,1,1] => [10] => [] => 1
[11] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11
[10,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 10
[9,2] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 17
[9,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 9
[8,3] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[8,2,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 15
[8,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
[7,4] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 22
[7,3,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 18
[7,2,2] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 19
[7,2,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 13
[7,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,5] => [2,2,2,2,2,1] => [2,2,2,2,1] => 20
[6,4,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 18
[6,3,2] => [3,3,2,1,1,1] => [3,2,1,1,1] => 24
[6,3,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 15
[6,2,2,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 16
[6,2,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 11
[6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,5,1] => [3,2,2,2,2] => [2,2,2,2] => 15
[5,4,2] => [3,3,2,2,1] => [3,2,2,1] => 23
[5,4,1,1] => [4,2,2,2,1] => [2,2,2,1] => 14
[5,3,3] => [3,3,3,1,1] => [3,3,1,1] => 22
[5,3,2,1] => [4,3,2,1,1] => [3,2,1,1] => 19
[5,3,1,1,1] => [5,2,2,1,1] => [2,2,1,1] => 12
[5,2,2,2] => [4,4,1,1,1] => [4,1,1,1] => 17
[5,2,2,1,1] => [5,3,1,1,1] => [3,1,1,1] => 13
[5,2,1,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => 9
[5,1,1,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => 5
[4,4,3] => [3,3,3,2] => [3,3,2] => 19
[4,4,2,1] => [4,3,2,2] => [3,2,2] => 16
[4,4,1,1,1] => [5,2,2,2] => [2,2,2] => 10
[4,3,3,1] => [4,3,3,1] => [3,3,1] => 16
[4,3,2,2] => [4,4,2,1] => [4,2,1] => 19
[4,3,2,1,1] => [5,3,2,1] => [3,2,1] => 14
[4,3,1,1,1,1] => [6,2,2,1] => [2,2,1] => 9
[4,2,2,2,1] => [5,4,1,1] => [4,1,1] => 13
[4,2,2,1,1,1] => [6,3,1,1] => [3,1,1] => 10
[4,2,1,1,1,1,1] => [7,2,1,1] => [2,1,1] => 7
[4,1,1,1,1,1,1,1] => [8,1,1,1] => [1,1,1] => 4
[3,3,3,2] => [4,4,3] => [4,3] => 14
[3,3,3,1,1] => [5,3,3] => [3,3] => 10
[3,3,2,2,1] => [5,4,2] => [4,2] => 12
[3,3,2,1,1,1] => [6,3,2] => [3,2] => 9
[3,3,1,1,1,1,1] => [7,2,2] => [2,2] => 6
[3,2,2,2,2] => [5,5,1] => [5,1] => 11
[3,2,2,2,1,1] => [6,4,1] => [4,1] => 9
[3,2,2,1,1,1,1] => [7,3,1] => [3,1] => 7
[3,2,1,1,1,1,1,1] => [8,2,1] => [2,1] => 5
[3,1,1,1,1,1,1,1,1] => [9,1,1] => [1,1] => 3
[2,2,2,2,2,1] => [6,5] => [5] => 6
[2,2,2,2,1,1,1] => [7,4] => [4] => 5
[2,2,2,1,1,1,1,1] => [8,3] => [3] => 4
[2,2,1,1,1,1,1,1,1] => [9,2] => [2] => 3
[2,1,1,1,1,1,1,1,1,1] => [10,1] => [1] => 2
[1,1,1,1,1,1,1,1,1,1,1] => [11] => [] => 1
[11,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11
[10,2] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 19
[10,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 10
[9,3] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 24
[9,2,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 17
[9,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 9
[8,4] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 26
[8,3,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[8,2,2] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 22
[8,2,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 15
[8,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
[7,5] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 25
[7,4,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 22
[7,3,2] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 29
[7,3,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 18
[7,2,2,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 19
[7,2,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 13
[7,1,1,1,1,1] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,6] => [2,2,2,2,2,2] => [2,2,2,2,2] => 21
[6,5,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 20
[6,4,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => 30
[6,4,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 18
[6,3,3] => [3,3,3,1,1,1] => [3,3,1,1,1] => 28
[6,3,2,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 24
[6,3,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 15
[6,2,2,2] => [4,4,1,1,1,1] => [4,1,1,1,1] => 21
[6,2,2,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 16
[6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 11
[6,1,1,1,1,1,1] => [7,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,5,2] => [3,3,2,2,2] => [3,2,2,2] => 25
[5,5,1,1] => [4,2,2,2,2] => [2,2,2,2] => 15
[5,4,3] => [3,3,3,2,1] => [3,3,2,1] => 28
[5,4,2,1] => [4,3,2,2,1] => [3,2,2,1] => 23
[5,4,1,1,1] => [5,2,2,2,1] => [2,2,2,1] => 14
[5,3,3,1] => [4,3,3,1,1] => [3,3,1,1] => 22
[5,3,2,2] => [4,4,2,1,1] => [4,2,1,1] => 26
[5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 19
[5,3,1,1,1,1] => [6,2,2,1,1] => [2,2,1,1] => 12
[5,2,2,2,1] => [5,4,1,1,1] => [4,1,1,1] => 17
[5,2,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => 13
[5,2,1,1,1,1,1] => [7,2,1,1,1] => [2,1,1,1] => 9
[5,1,1,1,1,1,1,1] => [8,1,1,1,1] => [1,1,1,1] => 5
[4,4,4] => [3,3,3,3] => [3,3,3] => 20
[4,4,3,1] => [4,3,3,2] => [3,3,2] => 19
[4,4,2,2] => [4,4,2,2] => [4,2,2] => 22
[4,4,2,1,1] => [5,3,2,2] => [3,2,2] => 16
[4,4,1,1,1,1] => [6,2,2,2] => [2,2,2] => 10
[4,3,3,2] => [4,4,3,1] => [4,3,1] => 23
[4,3,3,1,1] => [5,3,3,1] => [3,3,1] => 16
[4,3,2,2,1] => [5,4,2,1] => [4,2,1] => 19
[4,3,2,1,1,1] => [6,3,2,1] => [3,2,1] => 14
[4,3,1,1,1,1,1] => [7,2,2,1] => [2,2,1] => 9
[4,2,2,2,2] => [5,5,1,1] => [5,1,1] => 16
[4,2,2,2,1,1] => [6,4,1,1] => [4,1,1] => 13
[4,2,2,1,1,1,1] => [7,3,1,1] => [3,1,1] => 10
[4,2,1,1,1,1,1,1] => [8,2,1,1] => [2,1,1] => 7
[4,1,1,1,1,1,1,1,1] => [9,1,1,1] => [1,1,1] => 4
[3,3,3,3] => [4,4,4] => [4,4] => 15
[3,3,3,2,1] => [5,4,3] => [4,3] => 14
[3,3,3,1,1,1] => [6,3,3] => [3,3] => 10
[3,3,2,2,2] => [5,5,2] => [5,2] => 15
[3,3,2,2,1,1] => [6,4,2] => [4,2] => 12
[3,3,2,1,1,1,1] => [7,3,2] => [3,2] => 9
[3,3,1,1,1,1,1,1] => [8,2,2] => [2,2] => 6
[3,2,2,2,2,1] => [6,5,1] => [5,1] => 11
[3,2,2,2,1,1,1] => [7,4,1] => [4,1] => 9
[3,2,2,1,1,1,1,1] => [8,3,1] => [3,1] => 7
[3,2,1,1,1,1,1,1,1] => [9,2,1] => [2,1] => 5
[3,1,1,1,1,1,1,1,1,1] => [10,1,1] => [1,1] => 3
[2,2,2,2,2,2] => [6,6] => [6] => 7
[2,2,2,2,2,1,1] => [7,5] => [5] => 6
[2,2,2,2,1,1,1,1] => [8,4] => [4] => 5
[2,2,2,1,1,1,1,1,1] => [9,3] => [3] => 4
[2,2,1,1,1,1,1,1,1,1] => [10,2] => [2] => 3
[2,1,1,1,1,1,1,1,1,1,1] => [11,1] => [1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1] => [12] => [] => 1
[11,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11
[10,2,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 19
[10,1,1,1] => [4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 10
[9,3,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 24
[9,2,2] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 25
[9,2,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 17
[9,1,1,1,1] => [5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 9
[8,4,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 26
[8,3,2] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 34
[8,3,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[8,2,2,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 22
[8,2,1,1,1] => [5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 15
[8,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
[7,5,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 25
[7,4,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 37
[7,4,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => 22
[7,3,3] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 34
[7,3,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 29
[7,3,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => 18
[7,2,2,2] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => 25
[7,2,2,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => 19
[7,2,1,1,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => 13
[7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,6,1] => [3,2,2,2,2,2] => [2,2,2,2,2] => 21
[6,5,2] => [3,3,2,2,2,1] => [3,2,2,2,1] => 34
[6,5,1,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 20
[6,4,3] => [3,3,3,2,1,1] => [3,3,2,1,1] => 37
[6,4,2,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 30
[6,4,1,1,1] => [5,2,2,2,1,1] => [2,2,2,1,1] => 18
[6,3,3,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 28
[6,3,2,2] => [4,4,2,1,1,1] => [4,2,1,1,1] => 33
[6,3,2,1,1] => [5,3,2,1,1,1] => [3,2,1,1,1] => 24
[6,3,1,1,1,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => 15
[6,2,2,2,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => 21
[6,2,2,1,1,1] => [6,3,1,1,1,1] => [3,1,1,1,1] => 16
[6,2,1,1,1,1,1] => [7,2,1,1,1,1] => [2,1,1,1,1] => 11
[6,1,1,1,1,1,1,1] => [8,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,5,3] => [3,3,3,2,2] => [3,3,2,2] => 31
[5,5,2,1] => [4,3,2,2,2] => [3,2,2,2] => 25
[5,5,1,1,1] => [5,2,2,2,2] => [2,2,2,2] => 15
[5,4,4] => [3,3,3,3,1] => [3,3,3,1] => 30
[5,4,3,1] => [4,3,3,2,1] => [3,3,2,1] => 28
[5,4,2,2] => [4,4,2,2,1] => [4,2,2,1] => 32
[5,4,2,1,1] => [5,3,2,2,1] => [3,2,2,1] => 23
[5,4,1,1,1,1] => [6,2,2,2,1] => [2,2,2,1] => 14
[5,3,3,2] => [4,4,3,1,1] => [4,3,1,1] => 32
[5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 22
[5,3,2,2,1] => [5,4,2,1,1] => [4,2,1,1] => 26
[5,3,2,1,1,1] => [6,3,2,1,1] => [3,2,1,1] => 19
[5,3,1,1,1,1,1] => [7,2,2,1,1] => [2,2,1,1] => 12
[5,2,2,2,2] => [5,5,1,1,1] => [5,1,1,1] => 21
[5,2,2,2,1,1] => [6,4,1,1,1] => [4,1,1,1] => 17
[5,2,2,1,1,1,1] => [7,3,1,1,1] => [3,1,1,1] => 13
[5,2,1,1,1,1,1,1] => [8,2,1,1,1] => [2,1,1,1] => 9
[5,1,1,1,1,1,1,1,1] => [9,1,1,1,1] => [1,1,1,1] => 5
[4,4,4,1] => [4,3,3,3] => [3,3,3] => 20
[4,4,3,2] => [4,4,3,2] => [4,3,2] => 28
[4,4,3,1,1] => [5,3,3,2] => [3,3,2] => 19
[4,4,2,2,1] => [5,4,2,2] => [4,2,2] => 22
[4,4,2,1,1,1] => [6,3,2,2] => [3,2,2] => 16
[4,4,1,1,1,1,1] => [7,2,2,2] => [2,2,2] => 10
[4,3,3,3] => [4,4,4,1] => [4,4,1] => 25
[4,3,3,2,1] => [5,4,3,1] => [4,3,1] => 23
[4,3,3,1,1,1] => [6,3,3,1] => [3,3,1] => 16
[4,3,2,2,2] => [5,5,2,1] => [5,2,1] => 24
[4,3,2,2,1,1] => [6,4,2,1] => [4,2,1] => 19
[4,3,2,1,1,1,1] => [7,3,2,1] => [3,2,1] => 14
[4,3,1,1,1,1,1,1] => [8,2,2,1] => [2,2,1] => 9
[4,2,2,2,2,1] => [6,5,1,1] => [5,1,1] => 16
[4,2,2,2,1,1,1] => [7,4,1,1] => [4,1,1] => 13
[4,2,2,1,1,1,1,1] => [8,3,1,1] => [3,1,1] => 10
[4,2,1,1,1,1,1,1,1] => [9,2,1,1] => [2,1,1] => 7
[4,1,1,1,1,1,1,1,1,1] => [10,1,1,1] => [1,1,1] => 4
[3,3,3,3,1] => [5,4,4] => [4,4] => 15
[3,3,3,2,2] => [5,5,3] => [5,3] => 18
[3,3,3,2,1,1] => [6,4,3] => [4,3] => 14
[3,3,3,1,1,1,1] => [7,3,3] => [3,3] => 10
[3,3,2,2,2,1] => [6,5,2] => [5,2] => 15
[3,3,2,2,1,1,1] => [7,4,2] => [4,2] => 12
[3,3,2,1,1,1,1,1] => [8,3,2] => [3,2] => 9
[3,3,1,1,1,1,1,1,1] => [9,2,2] => [2,2] => 6
[3,2,2,2,2,2] => [6,6,1] => [6,1] => 13
[3,2,2,2,2,1,1] => [7,5,1] => [5,1] => 11
[3,2,2,2,1,1,1,1] => [8,4,1] => [4,1] => 9
[3,2,2,1,1,1,1,1,1] => [9,3,1] => [3,1] => 7
[3,2,1,1,1,1,1,1,1,1] => [10,2,1] => [2,1] => 5
[3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => [1,1] => 3
[2,2,2,2,2,2,1] => [7,6] => [6] => 7
[2,2,2,2,2,1,1,1] => [8,5] => [5] => 6
[2,2,2,2,1,1,1,1,1] => [9,4] => [4] => 5
[2,2,2,1,1,1,1,1,1,1] => [10,3] => [3] => 4
[2,2,1,1,1,1,1,1,1,1,1] => [11,2] => [2] => 3
[2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => [1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => [] => 1
[11,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11
[10,2,1,1] => [4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 19
[10,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 10
[9,3,1,1] => [4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 24
[9,2,2,1] => [4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 25
[9,2,1,1,1] => [5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 17
[9,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 9
[8,4,1,1] => [4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 26
[8,3,2,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 34
[8,3,1,1,1] => [5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[8,2,2,2] => [4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 29
[8,2,2,1,1] => [5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 22
[8,2,1,1,1,1] => [6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 15
[8,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
[7,5,1,1] => [4,2,2,2,2,1,1] => [2,2,2,2,1,1] => 25
[7,4,2,1] => [4,3,2,2,1,1,1] => [3,2,2,1,1,1] => 37
[7,4,1,1,1] => [5,2,2,2,1,1,1] => [2,2,2,1,1,1] => 22
[7,3,3,1] => [4,3,3,1,1,1,1] => [3,3,1,1,1,1] => 34
[7,3,2,2] => [4,4,2,1,1,1,1] => [4,2,1,1,1,1] => 40
[7,3,2,1,1] => [5,3,2,1,1,1,1] => [3,2,1,1,1,1] => 29
[7,3,1,1,1,1] => [6,2,2,1,1,1,1] => [2,2,1,1,1,1] => 18
[7,2,2,2,1] => [5,4,1,1,1,1,1] => [4,1,1,1,1,1] => 25
[7,2,2,1,1,1] => [6,3,1,1,1,1,1] => [3,1,1,1,1,1] => 19
[7,2,1,1,1,1,1] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => 13
[7,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,6,1,1] => [4,2,2,2,2,2] => [2,2,2,2,2] => 21
[6,5,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 34
[6,5,1,1,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 20
[6,4,3,1] => [4,3,3,2,1,1] => [3,3,2,1,1] => 37
[6,4,2,2] => [4,4,2,2,1,1] => [4,2,2,1,1] => 42
[6,4,2,1,1] => [5,3,2,2,1,1] => [3,2,2,1,1] => 30
[6,4,1,1,1,1] => [6,2,2,2,1,1] => [2,2,2,1,1] => 18
[6,3,3,2] => [4,4,3,1,1,1] => [4,3,1,1,1] => 41
[6,3,3,1,1] => [5,3,3,1,1,1] => [3,3,1,1,1] => 28
[6,3,2,2,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 33
[6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => 24
[6,3,1,1,1,1,1] => [7,2,2,1,1,1] => [2,2,1,1,1] => 15
[6,2,2,2,2] => [5,5,1,1,1,1] => [5,1,1,1,1] => 26
[6,2,2,2,1,1] => [6,4,1,1,1,1] => [4,1,1,1,1] => 21
[6,2,2,1,1,1,1] => [7,3,1,1,1,1] => [3,1,1,1,1] => 16
[6,2,1,1,1,1,1,1] => [8,2,1,1,1,1] => [2,1,1,1,1] => 11
[6,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,5,3,1] => [4,3,3,2,2] => [3,3,2,2] => 31
[5,5,2,2] => [4,4,2,2,2] => [4,2,2,2] => 35
[5,5,2,1,1] => [5,3,2,2,2] => [3,2,2,2] => 25
[5,5,1,1,1,1] => [6,2,2,2,2] => [2,2,2,2] => 15
[5,4,4,1] => [4,3,3,3,1] => [3,3,3,1] => 30
[5,4,3,2] => [4,4,3,2,1] => [4,3,2,1] => 42
[5,4,3,1,1] => [5,3,3,2,1] => [3,3,2,1] => 28
[5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 32
[5,4,2,1,1,1] => [6,3,2,2,1] => [3,2,2,1] => 23
[5,4,1,1,1,1,1] => [7,2,2,2,1] => [2,2,2,1] => 14
[5,3,3,3] => [4,4,4,1,1] => [4,4,1,1] => 35
[5,3,3,2,1] => [5,4,3,1,1] => [4,3,1,1] => 32
[5,3,3,1,1,1] => [6,3,3,1,1] => [3,3,1,1] => 22
[5,3,2,2,2] => [5,5,2,1,1] => [5,2,1,1] => 33
[5,3,2,2,1,1] => [6,4,2,1,1] => [4,2,1,1] => 26
[5,3,2,1,1,1,1] => [7,3,2,1,1] => [3,2,1,1] => 19
[5,3,1,1,1,1,1,1] => [8,2,2,1,1] => [2,2,1,1] => 12
[5,2,2,2,2,1] => [6,5,1,1,1] => [5,1,1,1] => 21
[5,2,2,2,1,1,1] => [7,4,1,1,1] => [4,1,1,1] => 17
[5,2,2,1,1,1,1,1] => [8,3,1,1,1] => [3,1,1,1] => 13
[5,2,1,1,1,1,1,1,1] => [9,2,1,1,1] => [2,1,1,1] => 9
[5,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1] => [1,1,1,1] => 5
[4,4,4,2] => [4,4,3,3] => [4,3,3] => 30
[4,4,4,1,1] => [5,3,3,3] => [3,3,3] => 20
[4,4,3,3] => [4,4,4,2] => [4,4,2] => 31
[4,4,3,2,1] => [5,4,3,2] => [4,3,2] => 28
[4,4,3,1,1,1] => [6,3,3,2] => [3,3,2] => 19
[4,4,2,2,2] => [5,5,2,2] => [5,2,2] => 28
[4,4,2,2,1,1] => [6,4,2,2] => [4,2,2] => 22
[4,4,2,1,1,1,1] => [7,3,2,2] => [3,2,2] => 16
[4,4,1,1,1,1,1,1] => [8,2,2,2] => [2,2,2] => 10
[4,3,3,3,1] => [5,4,4,1] => [4,4,1] => 25
[4,3,3,2,2] => [5,5,3,1] => [5,3,1] => 30
[4,3,3,2,1,1] => [6,4,3,1] => [4,3,1] => 23
[4,3,3,1,1,1,1] => [7,3,3,1] => [3,3,1] => 16
[4,3,2,2,2,1] => [6,5,2,1] => [5,2,1] => 24
[4,3,2,2,1,1,1] => [7,4,2,1] => [4,2,1] => 19
[4,3,2,1,1,1,1,1] => [8,3,2,1] => [3,2,1] => 14
[4,3,1,1,1,1,1,1,1] => [9,2,2,1] => [2,2,1] => 9
[4,2,2,2,2,2] => [6,6,1,1] => [6,1,1] => 19
[4,2,2,2,2,1,1] => [7,5,1,1] => [5,1,1] => 16
[4,2,2,2,1,1,1,1] => [8,4,1,1] => [4,1,1] => 13
[4,2,2,1,1,1,1,1,1] => [9,3,1,1] => [3,1,1] => 10
[4,2,1,1,1,1,1,1,1,1] => [10,2,1,1] => [2,1,1] => 7
[4,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1] => [1,1,1] => 4
[3,3,3,3,2] => [5,5,4] => [5,4] => 20
[3,3,3,3,1,1] => [6,4,4] => [4,4] => 15
[3,3,3,2,2,1] => [6,5,3] => [5,3] => 18
[3,3,3,2,1,1,1] => [7,4,3] => [4,3] => 14
[3,3,3,1,1,1,1,1] => [8,3,3] => [3,3] => 10
[3,3,2,2,2,2] => [6,6,2] => [6,2] => 18
[3,3,2,2,2,1,1] => [7,5,2] => [5,2] => 15
[3,3,2,2,1,1,1,1] => [8,4,2] => [4,2] => 12
[3,3,2,1,1,1,1,1,1] => [9,3,2] => [3,2] => 9
[3,3,1,1,1,1,1,1,1,1] => [10,2,2] => [2,2] => 6
[3,2,2,2,2,2,1] => [7,6,1] => [6,1] => 13
[3,2,2,2,2,1,1,1] => [8,5,1] => [5,1] => 11
[3,2,2,2,1,1,1,1,1] => [9,4,1] => [4,1] => 9
[3,2,2,1,1,1,1,1,1,1] => [10,3,1] => [3,1] => 7
[3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => [2,1] => 5
[3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => [1,1] => 3
[2,2,2,2,2,2,2] => [7,7] => [7] => 8
[2,2,2,2,2,2,1,1] => [8,6] => [6] => 7
[2,2,2,2,2,1,1,1,1] => [9,5] => [5] => 6
[2,2,2,2,1,1,1,1,1,1] => [10,4] => [4] => 5
[2,2,2,1,1,1,1,1,1,1,1] => [11,3] => [3] => 4
[2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => [2] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => [1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => [] => 1
[11,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11
[10,2,1,1,1] => [5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 19
[10,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 10
[9,3,1,1,1] => [5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 24
[9,2,2,1,1] => [5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 25
[9,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 17
[9,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 9
[8,4,1,1,1] => [5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 26
[8,3,2,1,1] => [5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 34
[8,3,1,1,1,1] => [6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[8,2,2,2,1] => [5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 29
[8,2,2,1,1,1] => [6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 22
[8,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 15
[8,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
[7,5,1,1,1] => [5,2,2,2,2,1,1] => [2,2,2,2,1,1] => 25
[7,4,2,1,1] => [5,3,2,2,1,1,1] => [3,2,2,1,1,1] => 37
[7,4,1,1,1,1] => [6,2,2,2,1,1,1] => [2,2,2,1,1,1] => 22
[7,3,3,1,1] => [5,3,3,1,1,1,1] => [3,3,1,1,1,1] => 34
[7,3,2,2,1] => [5,4,2,1,1,1,1] => [4,2,1,1,1,1] => 40
[7,3,2,1,1,1] => [6,3,2,1,1,1,1] => [3,2,1,1,1,1] => 29
[7,3,1,1,1,1,1] => [7,2,2,1,1,1,1] => [2,2,1,1,1,1] => 18
[7,2,2,2,2] => [5,5,1,1,1,1,1] => [5,1,1,1,1,1] => 31
[7,2,2,2,1,1] => [6,4,1,1,1,1,1] => [4,1,1,1,1,1] => 25
[7,2,2,1,1,1,1] => [7,3,1,1,1,1,1] => [3,1,1,1,1,1] => 19
[7,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1] => [2,1,1,1,1,1] => 13
[7,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,6,1,1,1] => [5,2,2,2,2,2] => [2,2,2,2,2] => 21
[6,5,2,1,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => 34
[6,5,1,1,1,1] => [6,2,2,2,2,1] => [2,2,2,2,1] => 20
[6,4,3,1,1] => [5,3,3,2,1,1] => [3,3,2,1,1] => 37
[6,4,2,2,1] => [5,4,2,2,1,1] => [4,2,2,1,1] => 42
[6,4,2,1,1,1] => [6,3,2,2,1,1] => [3,2,2,1,1] => 30
[6,4,1,1,1,1,1] => [7,2,2,2,1,1] => [2,2,2,1,1] => 18
[6,3,3,2,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => 41
[6,3,3,1,1,1] => [6,3,3,1,1,1] => [3,3,1,1,1] => 28
[6,3,2,2,2] => [5,5,2,1,1,1] => [5,2,1,1,1] => 42
[6,3,2,2,1,1] => [6,4,2,1,1,1] => [4,2,1,1,1] => 33
[6,3,2,1,1,1,1] => [7,3,2,1,1,1] => [3,2,1,1,1] => 24
[6,3,1,1,1,1,1,1] => [8,2,2,1,1,1] => [2,2,1,1,1] => 15
[6,2,2,2,2,1] => [6,5,1,1,1,1] => [5,1,1,1,1] => 26
[6,2,2,2,1,1,1] => [7,4,1,1,1,1] => [4,1,1,1,1] => 21
[6,2,2,1,1,1,1,1] => [8,3,1,1,1,1] => [3,1,1,1,1] => 16
[6,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1] => [2,1,1,1,1] => 11
[6,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,5,3,1,1] => [5,3,3,2,2] => [3,3,2,2] => 31
[5,5,2,2,1] => [5,4,2,2,2] => [4,2,2,2] => 35
[5,5,2,1,1,1] => [6,3,2,2,2] => [3,2,2,2] => 25
[5,5,1,1,1,1,1] => [7,2,2,2,2] => [2,2,2,2] => 15
[5,4,4,1,1] => [5,3,3,3,1] => [3,3,3,1] => 30
[5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 42
[5,4,3,1,1,1] => [6,3,3,2,1] => [3,3,2,1] => 28
[5,4,2,2,2] => [5,5,2,2,1] => [5,2,2,1] => 41
[5,4,2,2,1,1] => [6,4,2,2,1] => [4,2,2,1] => 32
[5,4,2,1,1,1,1] => [7,3,2,2,1] => [3,2,2,1] => 23
[5,4,1,1,1,1,1,1] => [8,2,2,2,1] => [2,2,2,1] => 14
[5,3,3,3,1] => [5,4,4,1,1] => [4,4,1,1] => 35
[5,3,3,2,2] => [5,5,3,1,1] => [5,3,1,1] => 42
[5,3,3,2,1,1] => [6,4,3,1,1] => [4,3,1,1] => 32
[5,3,3,1,1,1,1] => [7,3,3,1,1] => [3,3,1,1] => 22
[5,3,2,2,2,1] => [6,5,2,1,1] => [5,2,1,1] => 33
[5,3,2,2,1,1,1] => [7,4,2,1,1] => [4,2,1,1] => 26
[5,3,2,1,1,1,1,1] => [8,3,2,1,1] => [3,2,1,1] => 19
[5,3,1,1,1,1,1,1,1] => [9,2,2,1,1] => [2,2,1,1] => 12
[5,2,2,2,2,2] => [6,6,1,1,1] => [6,1,1,1] => 25
[5,2,2,2,2,1,1] => [7,5,1,1,1] => [5,1,1,1] => 21
[5,2,2,2,1,1,1,1] => [8,4,1,1,1] => [4,1,1,1] => 17
[5,2,2,1,1,1,1,1,1] => [9,3,1,1,1] => [3,1,1,1] => 13
[5,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1] => [2,1,1,1] => 9
[5,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1] => [1,1,1,1] => 5
[4,4,4,2,1] => [5,4,3,3] => [4,3,3] => 30
[4,4,4,1,1,1] => [6,3,3,3] => [3,3,3] => 20
[4,4,3,3,1] => [5,4,4,2] => [4,4,2] => 31
[4,4,3,2,2] => [5,5,3,2] => [5,3,2] => 37
[4,4,3,2,1,1] => [6,4,3,2] => [4,3,2] => 28
[4,4,3,1,1,1,1] => [7,3,3,2] => [3,3,2] => 19
[4,4,2,2,2,1] => [6,5,2,2] => [5,2,2] => 28
[4,4,2,2,1,1,1] => [7,4,2,2] => [4,2,2] => 22
[4,4,2,1,1,1,1,1] => [8,3,2,2] => [3,2,2] => 16
[4,4,1,1,1,1,1,1,1] => [9,2,2,2] => [2,2,2] => 10
[4,3,3,3,2] => [5,5,4,1] => [5,4,1] => 34
[4,3,3,3,1,1] => [6,4,4,1] => [4,4,1] => 25
[4,3,3,2,2,1] => [6,5,3,1] => [5,3,1] => 30
[4,3,3,2,1,1,1] => [7,4,3,1] => [4,3,1] => 23
[4,3,3,1,1,1,1,1] => [8,3,3,1] => [3,3,1] => 16
[4,3,2,2,2,2] => [6,6,2,1] => [6,2,1] => 29
[4,3,2,2,2,1,1] => [7,5,2,1] => [5,2,1] => 24
[4,3,2,2,1,1,1,1] => [8,4,2,1] => [4,2,1] => 19
[4,3,2,1,1,1,1,1,1] => [9,3,2,1] => [3,2,1] => 14
[4,3,1,1,1,1,1,1,1,1] => [10,2,2,1] => [2,2,1] => 9
[4,2,2,2,2,2,1] => [7,6,1,1] => [6,1,1] => 19
[4,2,2,2,2,1,1,1] => [8,5,1,1] => [5,1,1] => 16
[4,2,2,2,1,1,1,1,1] => [9,4,1,1] => [4,1,1] => 13
[4,2,2,1,1,1,1,1,1,1] => [10,3,1,1] => [3,1,1] => 10
[4,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1] => [2,1,1] => 7
[4,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1] => [1,1,1] => 4
[3,3,3,3,3] => [5,5,5] => [5,5] => 21
[3,3,3,3,2,1] => [6,5,4] => [5,4] => 20
[3,3,3,3,1,1,1] => [7,4,4] => [4,4] => 15
[3,3,3,2,2,2] => [6,6,3] => [6,3] => 22
[3,3,3,2,2,1,1] => [7,5,3] => [5,3] => 18
[3,3,3,2,1,1,1,1] => [8,4,3] => [4,3] => 14
[3,3,3,1,1,1,1,1,1] => [9,3,3] => [3,3] => 10
[3,3,2,2,2,2,1] => [7,6,2] => [6,2] => 18
[3,3,2,2,2,1,1,1] => [8,5,2] => [5,2] => 15
[3,3,2,2,1,1,1,1,1] => [9,4,2] => [4,2] => 12
[3,3,2,1,1,1,1,1,1,1] => [10,3,2] => [3,2] => 9
[3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => [2,2] => 6
[3,2,2,2,2,2,2] => [7,7,1] => [7,1] => 15
[3,2,2,2,2,2,1,1] => [8,6,1] => [6,1] => 13
[3,2,2,2,2,1,1,1,1] => [9,5,1] => [5,1] => 11
[3,2,2,2,1,1,1,1,1,1] => [10,4,1] => [4,1] => 9
[3,2,2,1,1,1,1,1,1,1,1] => [11,3,1] => [3,1] => 7
[3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1] => [2,1] => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1] => [1,1] => 3
[2,2,2,2,2,2,2,1] => [8,7] => [7] => 8
[2,2,2,2,2,2,1,1,1] => [9,6] => [6] => 7
[2,2,2,2,2,1,1,1,1,1] => [10,5] => [5] => 6
[2,2,2,2,1,1,1,1,1,1,1] => [11,4] => [4] => 5
[2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => [3] => 4
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2] => [2] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => [1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => [] => 1
[11,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11
[10,2,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 19
[10,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 10
[9,3,1,1,1,1] => [6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 24
[9,2,2,1,1,1] => [6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 25
[9,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 17
[9,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 9
[8,4,1,1,1,1] => [6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 26
[8,3,2,1,1,1] => [6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 34
[8,3,1,1,1,1,1] => [7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[8,2,2,2,1,1] => [6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 29
[8,2,2,1,1,1,1] => [7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 22
[8,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 15
[8,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
[7,5,1,1,1,1] => [6,2,2,2,2,1,1] => [2,2,2,2,1,1] => 25
[7,4,2,1,1,1] => [6,3,2,2,1,1,1] => [3,2,2,1,1,1] => 37
[7,4,1,1,1,1,1] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => 22
[7,3,3,1,1,1] => [6,3,3,1,1,1,1] => [3,3,1,1,1,1] => 34
[7,3,2,2,1,1] => [6,4,2,1,1,1,1] => [4,2,1,1,1,1] => 40
[7,3,2,1,1,1,1] => [7,3,2,1,1,1,1] => [3,2,1,1,1,1] => 29
[7,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => 18
[7,2,2,2,2,1] => [6,5,1,1,1,1,1] => [5,1,1,1,1,1] => 31
[7,2,2,2,1,1,1] => [7,4,1,1,1,1,1] => [4,1,1,1,1,1] => 25
[7,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1] => [3,1,1,1,1,1] => 19
[7,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1] => [2,1,1,1,1,1] => 13
[7,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,6,1,1,1,1] => [6,2,2,2,2,2] => [2,2,2,2,2] => 21
[6,5,2,1,1,1] => [6,3,2,2,2,1] => [3,2,2,2,1] => 34
[6,5,1,1,1,1,1] => [7,2,2,2,2,1] => [2,2,2,2,1] => 20
[6,4,3,1,1,1] => [6,3,3,2,1,1] => [3,3,2,1,1] => 37
[6,4,2,2,1,1] => [6,4,2,2,1,1] => [4,2,2,1,1] => 42
[6,4,2,1,1,1,1] => [7,3,2,2,1,1] => [3,2,2,1,1] => 30
[6,4,1,1,1,1,1,1] => [8,2,2,2,1,1] => [2,2,2,1,1] => 18
[6,3,3,2,1,1] => [6,4,3,1,1,1] => [4,3,1,1,1] => 41
[6,3,3,1,1,1,1] => [7,3,3,1,1,1] => [3,3,1,1,1] => 28
[6,3,2,2,2,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => 42
[6,3,2,2,1,1,1] => [7,4,2,1,1,1] => [4,2,1,1,1] => 33
[6,3,2,1,1,1,1,1] => [8,3,2,1,1,1] => [3,2,1,1,1] => 24
[6,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1] => [2,2,1,1,1] => 15
[6,2,2,2,2,2] => [6,6,1,1,1,1] => [6,1,1,1,1] => 31
[6,2,2,2,2,1,1] => [7,5,1,1,1,1] => [5,1,1,1,1] => 26
[6,2,2,2,1,1,1,1] => [8,4,1,1,1,1] => [4,1,1,1,1] => 21
[6,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1] => [3,1,1,1,1] => 16
[6,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1] => [2,1,1,1,1] => 11
[6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,5,3,1,1,1] => [6,3,3,2,2] => [3,3,2,2] => 31
[5,5,2,2,1,1] => [6,4,2,2,2] => [4,2,2,2] => 35
[5,5,2,1,1,1,1] => [7,3,2,2,2] => [3,2,2,2] => 25
[5,5,1,1,1,1,1,1] => [8,2,2,2,2] => [2,2,2,2] => 15
[5,4,4,1,1,1] => [6,3,3,3,1] => [3,3,3,1] => 30
[5,4,3,2,1,1] => [6,4,3,2,1] => [4,3,2,1] => 42
[5,4,3,1,1,1,1] => [7,3,3,2,1] => [3,3,2,1] => 28
[5,4,2,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => 41
[5,4,2,2,1,1,1] => [7,4,2,2,1] => [4,2,2,1] => 32
[5,4,2,1,1,1,1,1] => [8,3,2,2,1] => [3,2,2,1] => 23
[5,4,1,1,1,1,1,1,1] => [9,2,2,2,1] => [2,2,2,1] => 14
[5,3,3,3,1,1] => [6,4,4,1,1] => [4,4,1,1] => 35
[5,3,3,2,2,1] => [6,5,3,1,1] => [5,3,1,1] => 42
[5,3,3,2,1,1,1] => [7,4,3,1,1] => [4,3,1,1] => 32
[5,3,3,1,1,1,1,1] => [8,3,3,1,1] => [3,3,1,1] => 22
[5,3,2,2,2,2] => [6,6,2,1,1] => [6,2,1,1] => 40
[5,3,2,2,2,1,1] => [7,5,2,1,1] => [5,2,1,1] => 33
[5,3,2,2,1,1,1,1] => [8,4,2,1,1] => [4,2,1,1] => 26
[5,3,2,1,1,1,1,1,1] => [9,3,2,1,1] => [3,2,1,1] => 19
[5,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1] => [2,2,1,1] => 12
[5,2,2,2,2,2,1] => [7,6,1,1,1] => [6,1,1,1] => 25
[5,2,2,2,2,1,1,1] => [8,5,1,1,1] => [5,1,1,1] => 21
[5,2,2,2,1,1,1,1,1] => [9,4,1,1,1] => [4,1,1,1] => 17
[5,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1] => [3,1,1,1] => 13
[5,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1] => [2,1,1,1] => 9
[5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => [1,1,1,1] => 5
[4,4,4,2,1,1] => [6,4,3,3] => [4,3,3] => 30
[4,4,4,1,1,1,1] => [7,3,3,3] => [3,3,3] => 20
[4,4,3,3,1,1] => [6,4,4,2] => [4,4,2] => 31
[4,4,3,2,2,1] => [6,5,3,2] => [5,3,2] => 37
[4,4,3,2,1,1,1] => [7,4,3,2] => [4,3,2] => 28
[4,4,3,1,1,1,1,1] => [8,3,3,2] => [3,3,2] => 19
[4,4,2,2,2,2] => [6,6,2,2] => [6,2,2] => 34
[4,4,2,2,2,1,1] => [7,5,2,2] => [5,2,2] => 28
[4,4,2,2,1,1,1,1] => [8,4,2,2] => [4,2,2] => 22
[4,4,2,1,1,1,1,1,1] => [9,3,2,2] => [3,2,2] => 16
[4,4,1,1,1,1,1,1,1,1] => [10,2,2,2] => [2,2,2] => 10
[4,3,3,3,2,1] => [6,5,4,1] => [5,4,1] => 34
[4,3,3,3,1,1,1] => [7,4,4,1] => [4,4,1] => 25
[4,3,3,2,2,2] => [6,6,3,1] => [6,3,1] => 37
[4,3,3,2,2,1,1] => [7,5,3,1] => [5,3,1] => 30
[4,3,3,2,1,1,1,1] => [8,4,3,1] => [4,3,1] => 23
[4,3,3,1,1,1,1,1,1] => [9,3,3,1] => [3,3,1] => 16
[4,3,2,2,2,2,1] => [7,6,2,1] => [6,2,1] => 29
[4,3,2,2,2,1,1,1] => [8,5,2,1] => [5,2,1] => 24
[4,3,2,2,1,1,1,1,1] => [9,4,2,1] => [4,2,1] => 19
[4,3,2,1,1,1,1,1,1,1] => [10,3,2,1] => [3,2,1] => 14
[4,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1] => [2,2,1] => 9
[4,2,2,2,2,2,2] => [7,7,1,1] => [7,1,1] => 22
[4,2,2,2,2,2,1,1] => [8,6,1,1] => [6,1,1] => 19
[4,2,2,2,2,1,1,1,1] => [9,5,1,1] => [5,1,1] => 16
[4,2,2,2,1,1,1,1,1,1] => [10,4,1,1] => [4,1,1] => 13
[4,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1] => [3,1,1] => 10
[4,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1] => [2,1,1] => 7
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1] => [1,1,1] => 4
[3,3,3,3,3,1] => [6,5,5] => [5,5] => 21
[3,3,3,3,2,2] => [6,6,4] => [6,4] => 25
[3,3,3,3,2,1,1] => [7,5,4] => [5,4] => 20
[3,3,3,3,1,1,1,1] => [8,4,4] => [4,4] => 15
[3,3,3,2,2,2,1] => [7,6,3] => [6,3] => 22
[3,3,3,2,2,1,1,1] => [8,5,3] => [5,3] => 18
[3,3,3,2,1,1,1,1,1] => [9,4,3] => [4,3] => 14
[3,3,3,1,1,1,1,1,1,1] => [10,3,3] => [3,3] => 10
[3,3,2,2,2,2,2] => [7,7,2] => [7,2] => 21
[3,3,2,2,2,2,1,1] => [8,6,2] => [6,2] => 18
[3,3,2,2,2,1,1,1,1] => [9,5,2] => [5,2] => 15
[3,3,2,2,1,1,1,1,1,1] => [10,4,2] => [4,2] => 12
[3,3,2,1,1,1,1,1,1,1,1] => [11,3,2] => [3,2] => 9
[3,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2] => [2,2] => 6
[3,2,2,2,2,2,2,1] => [8,7,1] => [7,1] => 15
[3,2,2,2,2,2,1,1,1] => [9,6,1] => [6,1] => 13
[3,2,2,2,2,1,1,1,1,1] => [10,5,1] => [5,1] => 11
[3,2,2,2,1,1,1,1,1,1,1] => [11,4,1] => [4,1] => 9
[3,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1] => [3,1] => 7
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1] => [2,1] => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1] => [1,1] => 3
[2,2,2,2,2,2,2,2] => [8,8] => [8] => 9
[2,2,2,2,2,2,2,1,1] => [9,7] => [7] => 8
[2,2,2,2,2,2,1,1,1,1] => [10,6] => [6] => 7
[2,2,2,2,2,1,1,1,1,1,1] => [11,5] => [5] => 6
[2,2,2,2,1,1,1,1,1,1,1,1] => [12,4] => [4] => 5
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3] => [3] => 4
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2] => [2] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1] => [1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16] => [] => 1
[11,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11
[10,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 19
[10,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 10
[9,3,1,1,1,1,1] => [7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 24
[9,2,2,1,1,1,1] => [7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 25
[9,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 17
[9,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 9
[8,4,1,1,1,1,1] => [7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 26
[8,3,2,1,1,1,1] => [7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 34
[8,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[8,2,2,2,1,1,1] => [7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 29
[8,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 22
[8,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 15
[8,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
[7,5,1,1,1,1,1] => [7,2,2,2,2,1,1] => [2,2,2,2,1,1] => 25
[7,4,2,1,1,1,1] => [7,3,2,2,1,1,1] => [3,2,2,1,1,1] => 37
[7,4,1,1,1,1,1,1] => [8,2,2,2,1,1,1] => [2,2,2,1,1,1] => 22
[7,3,3,1,1,1,1] => [7,3,3,1,1,1,1] => [3,3,1,1,1,1] => 34
[7,3,2,2,1,1,1] => [7,4,2,1,1,1,1] => [4,2,1,1,1,1] => 40
[7,3,2,1,1,1,1,1] => [8,3,2,1,1,1,1] => [3,2,1,1,1,1] => 29
[7,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1,1] => [2,2,1,1,1,1] => 18
[7,2,2,2,2,1,1] => [7,5,1,1,1,1,1] => [5,1,1,1,1,1] => 31
[7,2,2,2,1,1,1,1] => [8,4,1,1,1,1,1] => [4,1,1,1,1,1] => 25
[7,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1,1] => [3,1,1,1,1,1] => 19
[7,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1,1] => [2,1,1,1,1,1] => 13
[7,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
[6,6,1,1,1,1,1] => [7,2,2,2,2,2] => [2,2,2,2,2] => 21
[6,5,2,1,1,1,1] => [7,3,2,2,2,1] => [3,2,2,2,1] => 34
[6,5,1,1,1,1,1,1] => [8,2,2,2,2,1] => [2,2,2,2,1] => 20
[6,4,3,1,1,1,1] => [7,3,3,2,1,1] => [3,3,2,1,1] => 37
[6,4,2,2,1,1,1] => [7,4,2,2,1,1] => [4,2,2,1,1] => 42
[6,4,2,1,1,1,1,1] => [8,3,2,2,1,1] => [3,2,2,1,1] => 30
[6,4,1,1,1,1,1,1,1] => [9,2,2,2,1,1] => [2,2,2,1,1] => 18
[6,3,3,2,1,1,1] => [7,4,3,1,1,1] => [4,3,1,1,1] => 41
[6,3,3,1,1,1,1,1] => [8,3,3,1,1,1] => [3,3,1,1,1] => 28
[6,3,2,2,2,1,1] => [7,5,2,1,1,1] => [5,2,1,1,1] => 42
[6,3,2,2,1,1,1,1] => [8,4,2,1,1,1] => [4,2,1,1,1] => 33
[6,3,2,1,1,1,1,1,1] => [9,3,2,1,1,1] => [3,2,1,1,1] => 24
[6,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1,1] => [2,2,1,1,1] => 15
[6,2,2,2,2,2,1] => [7,6,1,1,1,1] => [6,1,1,1,1] => 31
[6,2,2,2,2,1,1,1] => [8,5,1,1,1,1] => [5,1,1,1,1] => 26
[6,2,2,2,1,1,1,1,1] => [9,4,1,1,1,1] => [4,1,1,1,1] => 21
[6,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1,1] => [3,1,1,1,1] => 16
[6,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1,1] => [2,1,1,1,1] => 11
[6,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1,1] => [1,1,1,1,1] => 6
[5,5,3,1,1,1,1] => [7,3,3,2,2] => [3,3,2,2] => 31
[5,5,2,2,1,1,1] => [7,4,2,2,2] => [4,2,2,2] => 35
[5,5,2,1,1,1,1,1] => [8,3,2,2,2] => [3,2,2,2] => 25
[5,5,1,1,1,1,1,1,1] => [9,2,2,2,2] => [2,2,2,2] => 15
[5,4,4,1,1,1,1] => [7,3,3,3,1] => [3,3,3,1] => 30
[5,4,3,2,1,1,1] => [7,4,3,2,1] => [4,3,2,1] => 42
[5,4,3,1,1,1,1,1] => [8,3,3,2,1] => [3,3,2,1] => 28
[5,4,2,2,2,1,1] => [7,5,2,2,1] => [5,2,2,1] => 41
[5,4,2,2,1,1,1,1] => [8,4,2,2,1] => [4,2,2,1] => 32
[5,4,2,1,1,1,1,1,1] => [9,3,2,2,1] => [3,2,2,1] => 23
[5,4,1,1,1,1,1,1,1,1] => [10,2,2,2,1] => [2,2,2,1] => 14
[5,3,3,3,1,1,1] => [7,4,4,1,1] => [4,4,1,1] => 35
[5,3,3,2,2,1,1] => [7,5,3,1,1] => [5,3,1,1] => 42
[5,3,3,2,1,1,1,1] => [8,4,3,1,1] => [4,3,1,1] => 32
[5,3,3,1,1,1,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => 22
[5,3,2,2,2,2,1] => [7,6,2,1,1] => [6,2,1,1] => 40
[5,3,2,2,2,1,1,1] => [8,5,2,1,1] => [5,2,1,1] => 33
[5,3,2,2,1,1,1,1,1] => [9,4,2,1,1] => [4,2,1,1] => 26
[5,3,2,1,1,1,1,1,1,1] => [10,3,2,1,1] => [3,2,1,1] => 19
[5,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1,1] => [2,2,1,1] => 12
[5,2,2,2,2,2,2] => [7,7,1,1,1] => [7,1,1,1] => 29
[5,2,2,2,2,2,1,1] => [8,6,1,1,1] => [6,1,1,1] => 25
[5,2,2,2,2,1,1,1,1] => [9,5,1,1,1] => [5,1,1,1] => 21
[5,2,2,2,1,1,1,1,1,1] => [10,4,1,1,1] => [4,1,1,1] => 17
[5,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1,1] => [3,1,1,1] => 13
[5,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1,1] => [2,1,1,1] => 9
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1] => [1,1,1,1] => 5
[4,4,4,2,1,1,1] => [7,4,3,3] => [4,3,3] => 30
[4,4,4,1,1,1,1,1] => [8,3,3,3] => [3,3,3] => 20
[4,4,3,3,1,1,1] => [7,4,4,2] => [4,4,2] => 31
[4,4,3,2,2,1,1] => [7,5,3,2] => [5,3,2] => 37
[4,4,3,2,1,1,1,1] => [8,4,3,2] => [4,3,2] => 28
[4,4,3,1,1,1,1,1,1] => [9,3,3,2] => [3,3,2] => 19
[4,4,2,2,2,2,1] => [7,6,2,2] => [6,2,2] => 34
[4,4,2,2,2,1,1,1] => [8,5,2,2] => [5,2,2] => 28
[4,4,2,2,1,1,1,1,1] => [9,4,2,2] => [4,2,2] => 22
[4,4,2,1,1,1,1,1,1,1] => [10,3,2,2] => [3,2,2] => 16
[4,4,1,1,1,1,1,1,1,1,1] => [11,2,2,2] => [2,2,2] => 10
[4,3,3,3,2,1,1] => [7,5,4,1] => [5,4,1] => 34
[4,3,3,3,1,1,1,1] => [8,4,4,1] => [4,4,1] => 25
[4,3,3,2,2,2,1] => [7,6,3,1] => [6,3,1] => 37
[4,3,3,2,2,1,1,1] => [8,5,3,1] => [5,3,1] => 30
[4,3,3,2,1,1,1,1,1] => [9,4,3,1] => [4,3,1] => 23
[4,3,3,1,1,1,1,1,1,1] => [10,3,3,1] => [3,3,1] => 16
[4,3,2,2,2,2,2] => [7,7,2,1] => [7,2,1] => 34
[4,3,2,2,2,2,1,1] => [8,6,2,1] => [6,2,1] => 29
[4,3,2,2,2,1,1,1,1] => [9,5,2,1] => [5,2,1] => 24
[4,3,2,2,1,1,1,1,1,1] => [10,4,2,1] => [4,2,1] => 19
[4,3,2,1,1,1,1,1,1,1,1] => [11,3,2,1] => [3,2,1] => 14
[4,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2,1] => [2,2,1] => 9
[4,2,2,2,2,2,2,1] => [8,7,1,1] => [7,1,1] => 22
[4,2,2,2,2,2,1,1,1] => [9,6,1,1] => [6,1,1] => 19
[4,2,2,2,2,1,1,1,1,1] => [10,5,1,1] => [5,1,1] => 16
[4,2,2,2,1,1,1,1,1,1,1] => [11,4,1,1] => [4,1,1] => 13
[4,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1,1] => [3,1,1] => 10
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1,1] => [2,1,1] => 7
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1,1] => [1,1,1] => 4
[3,3,3,3,3,1,1] => [7,5,5] => [5,5] => 21
[3,3,3,3,2,2,1] => [7,6,4] => [6,4] => 25
[3,3,3,3,2,1,1,1] => [8,5,4] => [5,4] => 20
[3,3,3,3,1,1,1,1,1] => [9,4,4] => [4,4] => 15
[3,3,3,2,2,2,2] => [7,7,3] => [7,3] => 26
[3,3,3,2,2,2,1,1] => [8,6,3] => [6,3] => 22
[3,3,3,2,2,1,1,1,1] => [9,5,3] => [5,3] => 18
[3,3,3,2,1,1,1,1,1,1] => [10,4,3] => [4,3] => 14
[3,3,3,1,1,1,1,1,1,1,1] => [11,3,3] => [3,3] => 10
[3,3,2,2,2,2,2,1] => [8,7,2] => [7,2] => 21
[3,3,2,2,2,2,1,1,1] => [9,6,2] => [6,2] => 18
[3,3,2,2,2,1,1,1,1,1] => [10,5,2] => [5,2] => 15
[3,3,2,2,1,1,1,1,1,1,1] => [11,4,2] => [4,2] => 12
[3,3,2,1,1,1,1,1,1,1,1,1] => [12,3,2] => [3,2] => 9
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2] => [2,2] => 6
[3,2,2,2,2,2,2,2] => [8,8,1] => [8,1] => 17
[3,2,2,2,2,2,2,1,1] => [9,7,1] => [7,1] => 15
[3,2,2,2,2,2,1,1,1,1] => [10,6,1] => [6,1] => 13
[3,2,2,2,2,1,1,1,1,1,1] => [11,5,1] => [5,1] => 11
[3,2,2,2,1,1,1,1,1,1,1,1] => [12,4,1] => [4,1] => 9
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3,1] => [3,1] => 7
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2,1] => [2,1] => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1,1] => [1,1] => 3
[2,2,2,2,2,2,2,2,1] => [9,8] => [8] => 9
[2,2,2,2,2,2,2,1,1,1] => [10,7] => [7] => 8
[2,2,2,2,2,2,1,1,1,1,1] => [11,6] => [6] => 7
[2,2,2,2,2,1,1,1,1,1,1,1] => [12,5] => [5] => 6
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [13,4] => [4] => 5
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [14,3] => [3] => 4
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,2] => [2] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16,1] => [1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [17] => [] => 1
[2,2,2,2,2,2,2,2,2] => [9,9] => [9] => 10
[3,3,3,3,2,2,1,1,1,1] => [10,6,4] => [6,4] => 25
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,1 1,1,2,1 1,1,2,1,2 1,1,2,2,2,2,1 1,1,2,2,2,2,3,0,2 1,1,2,2,3,2,3,1,3,2,1,1 1,1,2,2,3,2,3,1,5,3,1,1,2,2,1 1,1,2,2,3,3,3,1,5,4,1,2,3,2,3,3,0,2,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + q^{2} + q^{3}$
$F_{4} = q + q^{2} + 2\ q^{3} + q^{4}$
$F_{5} = q + q^{2} + 2\ q^{3} + q^{4} + 2\ q^{5}$
$F_{6} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 2\ q^{5} + 2\ q^{6} + q^{7}$
$F_{7} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 2\ q^{5} + 2\ q^{6} + 3\ q^{7} + 2\ q^{9}$
$F_{8} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 2\ q^{6} + 3\ q^{7} + q^{8} + 3\ q^{9} + 2\ q^{10} + q^{11} + q^{12}$
$F_{9} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 2\ q^{6} + 3\ q^{7} + q^{8} + 5\ q^{9} + 3\ q^{10} + q^{11} + q^{12} + 2\ q^{13} + 2\ q^{14} + q^{15}$
$F_{10} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 3\ q^{6} + 3\ q^{7} + q^{8} + 5\ q^{9} + 4\ q^{10} + q^{11} + 2\ q^{12} + 3\ q^{13} + 2\ q^{14} + 3\ q^{15} + 3\ q^{16} + 2\ q^{18} + q^{19}$
$F_{11} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 3\ q^{6} + 3\ q^{7} + q^{8} + 5\ q^{9} + 4\ q^{10} + 3\ q^{11} + 2\ q^{12} + 3\ q^{13} + 3\ q^{14} + 3\ q^{15} + 3\ q^{16} + 2\ q^{17} + 2\ q^{18} + 4\ q^{19} + q^{20} + q^{21} + 2\ q^{22} + q^{23} + q^{24}$
Description
The number of partitions contained in the given partition.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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