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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
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-----------------------------------------------------------------------------
Statistic identifier: St001389
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of partitions of the same length below the given integer partition.
For a partition $\lambda_1 \geq \dots \lambda_k > 0$, this number is
$$ \det\left( \binom{\lambda_{k+1-i}}{j-i+1} \right)_{1 \le i,j \le k}.$$
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(la):
k = len(la)
return det(matrix([[binomial(la[k-i], j-i+1) for j in range(1, k+1)] for i in range(1, k+1)]))
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 2
[1,1] => 1
[3] => 3
[2,1] => 2
[1,1,1] => 1
[4] => 4
[3,1] => 3
[2,2] => 3
[2,1,1] => 2
[1,1,1,1] => 1
[5] => 5
[4,1] => 4
[3,2] => 5
[3,1,1] => 3
[2,2,1] => 3
[2,1,1,1] => 2
[1,1,1,1,1] => 1
[6] => 6
[5,1] => 5
[4,2] => 7
[4,1,1] => 4
[3,3] => 6
[3,2,1] => 5
[3,1,1,1] => 3
[2,2,2] => 4
[2,2,1,1] => 3
[2,1,1,1,1] => 2
[1,1,1,1,1,1] => 1
[7] => 7
[6,1] => 6
[5,2] => 9
[5,1,1] => 5
[4,3] => 9
[4,2,1] => 7
[4,1,1,1] => 4
[3,3,1] => 6
[3,2,2] => 7
[3,2,1,1] => 5
[3,1,1,1,1] => 3
[2,2,2,1] => 4
[2,2,1,1,1] => 3
[2,1,1,1,1,1] => 2
[1,1,1,1,1,1,1] => 1
[8] => 8
[7,1] => 7
[6,2] => 11
[6,1,1] => 6
[5,3] => 12
[5,2,1] => 9
[5,1,1,1] => 5
[4,4] => 10
[4,3,1] => 9
[4,2,2] => 10
[4,2,1,1] => 7
[4,1,1,1,1] => 4
[3,3,2] => 9
[3,3,1,1] => 6
[3,2,2,1] => 7
[3,2,1,1,1] => 5
[3,1,1,1,1,1] => 3
[2,2,2,2] => 5
[2,2,2,1,1] => 4
[2,2,1,1,1,1] => 3
[2,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1] => 1
[9] => 9
[8,1] => 8
[7,2] => 13
[7,1,1] => 7
[6,3] => 15
[6,2,1] => 11
[6,1,1,1] => 6
[5,4] => 14
[5,3,1] => 12
[5,2,2] => 13
[5,2,1,1] => 9
[5,1,1,1,1] => 5
[4,4,1] => 10
[4,3,2] => 14
[4,3,1,1] => 9
[4,2,2,1] => 10
[4,2,1,1,1] => 7
[4,1,1,1,1,1] => 4
[3,3,3] => 10
[3,3,2,1] => 9
[3,3,1,1,1] => 6
[3,2,2,2] => 9
[3,2,2,1,1] => 7
[3,2,1,1,1,1] => 5
[3,1,1,1,1,1,1] => 3
[2,2,2,2,1] => 5
[2,2,2,1,1,1] => 4
[2,2,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1] => 1
[10] => 10
[9,1] => 9
[8,2] => 15
[8,1,1] => 8
[7,3] => 18
[7,2,1] => 13
[7,1,1,1] => 7
[6,4] => 18
[6,3,1] => 15
[6,2,2] => 16
[6,2,1,1] => 11
[6,1,1,1,1] => 6
[5,5] => 15
[5,4,1] => 14
[5,3,2] => 19
[5,3,1,1] => 12
[5,2,2,1] => 13
[5,2,1,1,1] => 9
[5,1,1,1,1,1] => 5
[4,4,2] => 16
[4,4,1,1] => 10
[4,3,3] => 16
[4,3,2,1] => 14
[4,3,1,1,1] => 9
[4,2,2,2] => 13
[4,2,2,1,1] => 10
[4,2,1,1,1,1] => 7
[4,1,1,1,1,1,1] => 4
[3,3,3,1] => 10
[3,3,2,2] => 12
[3,3,2,1,1] => 9
[3,3,1,1,1,1] => 6
[3,2,2,2,1] => 9
[3,2,2,1,1,1] => 7
[3,2,1,1,1,1,1] => 5
[3,1,1,1,1,1,1,1] => 3
[2,2,2,2,2] => 6
[2,2,2,2,1,1] => 5
[2,2,2,1,1,1,1] => 4
[2,2,1,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1] => 1
[11] => 11
[10,1] => 10
[9,2] => 17
[9,1,1] => 9
[8,3] => 21
[8,2,1] => 15
[8,1,1,1] => 8
[7,4] => 22
[7,3,1] => 18
[7,2,2] => 19
[7,2,1,1] => 13
[7,1,1,1,1] => 7
[6,5] => 20
[6,4,1] => 18
[6,3,2] => 24
[6,3,1,1] => 15
[6,2,2,1] => 16
[6,2,1,1,1] => 11
[6,1,1,1,1,1] => 6
[5,5,1] => 15
[5,4,2] => 23
[5,4,1,1] => 14
[5,3,3] => 22
[5,3,2,1] => 19
[5,3,1,1,1] => 12
[5,2,2,2] => 17
[5,2,2,1,1] => 13
[5,2,1,1,1,1] => 9
[5,1,1,1,1,1,1] => 5
[4,4,3] => 19
[4,4,2,1] => 16
[4,4,1,1,1] => 10
[4,3,3,1] => 16
[4,3,2,2] => 19
[4,3,2,1,1] => 14
[4,3,1,1,1,1] => 9
[4,2,2,2,1] => 13
[4,2,2,1,1,1] => 10
[4,2,1,1,1,1,1] => 7
[4,1,1,1,1,1,1,1] => 4
[3,3,3,2] => 14
[3,3,3,1,1] => 10
[3,3,2,2,1] => 12
[3,3,2,1,1,1] => 9
[3,3,1,1,1,1,1] => 6
[3,2,2,2,2] => 11
[3,2,2,2,1,1] => 9
[3,2,2,1,1,1,1] => 7
[3,2,1,1,1,1,1,1] => 5
[3,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,1] => 6
[2,2,2,2,1,1,1] => 5
[2,2,2,1,1,1,1,1] => 4
[2,2,1,1,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1] => 1
[12] => 12
[11,1] => 11
[10,2] => 19
[10,1,1] => 10
[9,3] => 24
[9,2,1] => 17
[9,1,1,1] => 9
[8,4] => 26
[8,3,1] => 21
[8,2,2] => 22
[8,2,1,1] => 15
[8,1,1,1,1] => 8
[7,5] => 25
[7,4,1] => 22
[7,3,2] => 29
[7,3,1,1] => 18
[7,2,2,1] => 19
[7,2,1,1,1] => 13
[7,1,1,1,1,1] => 7
[6,6] => 21
[6,5,1] => 20
[6,4,2] => 30
[6,4,1,1] => 18
[6,3,3] => 28
[6,3,2,1] => 24
[6,3,1,1,1] => 15
[6,2,2,2] => 21
[6,2,2,1,1] => 16
[6,2,1,1,1,1] => 11
[6,1,1,1,1,1,1] => 6
[5,5,2] => 25
[5,5,1,1] => 15
[5,4,3] => 28
[5,4,2,1] => 23
[5,4,1,1,1] => 14
[5,3,3,1] => 22
[5,3,2,2] => 26
[5,3,2,1,1] => 19
[5,3,1,1,1,1] => 12
[5,2,2,2,1] => 17
[5,2,2,1,1,1] => 13
[5,2,1,1,1,1,1] => 9
[5,1,1,1,1,1,1,1] => 5
[4,4,4] => 20
[4,4,3,1] => 19
[4,4,2,2] => 22
[4,4,2,1,1] => 16
[4,4,1,1,1,1] => 10
[4,3,3,2] => 23
[4,3,3,1,1] => 16
[4,3,2,2,1] => 19
[4,3,2,1,1,1] => 14
[4,3,1,1,1,1,1] => 9
[4,2,2,2,2] => 16
[4,2,2,2,1,1] => 13
[4,2,2,1,1,1,1] => 10
[4,2,1,1,1,1,1,1] => 7
[4,1,1,1,1,1,1,1,1] => 4
[3,3,3,3] => 15
[3,3,3,2,1] => 14
[3,3,3,1,1,1] => 10
[3,3,2,2,2] => 15
[3,3,2,2,1,1] => 12
[3,3,2,1,1,1,1] => 9
[3,3,1,1,1,1,1,1] => 6
[3,2,2,2,2,1] => 11
[3,2,2,2,1,1,1] => 9
[3,2,2,1,1,1,1,1] => 7
[3,2,1,1,1,1,1,1,1] => 5
[3,1,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,2] => 7
[2,2,2,2,2,1,1] => 6
[2,2,2,2,1,1,1,1] => 5
[2,2,2,1,1,1,1,1,1] => 4
[2,2,1,1,1,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1] => 1
[13] => 13
[12,1] => 12
[11,2] => 21
[11,1,1] => 11
[10,3] => 27
[10,2,1] => 19
[10,1,1,1] => 10
[9,4] => 30
[9,3,1] => 24
[9,2,2] => 25
[9,2,1,1] => 17
[9,1,1,1,1] => 9
[8,5] => 30
[8,4,1] => 26
[8,3,2] => 34
[8,3,1,1] => 21
[8,2,2,1] => 22
[8,2,1,1,1] => 15
[8,1,1,1,1,1] => 8
[7,6] => 27
[7,5,1] => 25
[7,4,2] => 37
[7,4,1,1] => 22
[7,3,3] => 34
[7,3,2,1] => 29
[7,3,1,1,1] => 18
[7,2,2,2] => 25
[7,2,2,1,1] => 19
[7,2,1,1,1,1] => 13
[7,1,1,1,1,1,1] => 7
[6,6,1] => 21
[6,5,2] => 34
[6,5,1,1] => 20
[6,4,3] => 37
[6,4,2,1] => 30
[6,4,1,1,1] => 18
[6,3,3,1] => 28
[6,3,2,2] => 33
[6,3,2,1,1] => 24
[6,3,1,1,1,1] => 15
[6,2,2,2,1] => 21
[6,2,2,1,1,1] => 16
[6,2,1,1,1,1,1] => 11
[6,1,1,1,1,1,1,1] => 6
[5,5,3] => 31
[5,5,2,1] => 25
[5,5,1,1,1] => 15
[5,4,4] => 30
[5,4,3,1] => 28
[5,4,2,2] => 32
[5,4,2,1,1] => 23
[5,4,1,1,1,1] => 14
[5,3,3,2] => 32
[5,3,3,1,1] => 22
[5,3,2,2,1] => 26
[5,3,2,1,1,1] => 19
[5,3,1,1,1,1,1] => 12
[5,2,2,2,2] => 21
[5,2,2,2,1,1] => 17
[5,2,2,1,1,1,1] => 13
[5,2,1,1,1,1,1,1] => 9
[5,1,1,1,1,1,1,1,1] => 5
[4,4,4,1] => 20
[4,4,3,2] => 28
[4,4,3,1,1] => 19
[4,4,2,2,1] => 22
[4,4,2,1,1,1] => 16
[4,4,1,1,1,1,1] => 10
[4,3,3,3] => 25
[4,3,3,2,1] => 23
[4,3,3,1,1,1] => 16
[4,3,2,2,2] => 24
[4,3,2,2,1,1] => 19
[4,3,2,1,1,1,1] => 14
[4,3,1,1,1,1,1,1] => 9
[4,2,2,2,2,1] => 16
[4,2,2,2,1,1,1] => 13
[4,2,2,1,1,1,1,1] => 10
[4,2,1,1,1,1,1,1,1] => 7
[4,1,1,1,1,1,1,1,1,1] => 4
[3,3,3,3,1] => 15
[3,3,3,2,2] => 18
[3,3,3,2,1,1] => 14
[3,3,3,1,1,1,1] => 10
[3,3,2,2,2,1] => 15
[3,3,2,2,1,1,1] => 12
[3,3,2,1,1,1,1,1] => 9
[3,3,1,1,1,1,1,1,1] => 6
[3,2,2,2,2,2] => 13
[3,2,2,2,2,1,1] => 11
[3,2,2,2,1,1,1,1] => 9
[3,2,2,1,1,1,1,1,1] => 7
[3,2,1,1,1,1,1,1,1,1] => 5
[3,1,1,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,2,1] => 7
[2,2,2,2,2,1,1,1] => 6
[2,2,2,2,1,1,1,1,1] => 5
[2,2,2,1,1,1,1,1,1,1] => 4
[2,2,1,1,1,1,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[14] => 14
[13,1] => 13
[12,2] => 23
[12,1,1] => 12
[11,3] => 30
[11,2,1] => 21
[11,1,1,1] => 11
[10,4] => 34
[10,3,1] => 27
[10,2,2] => 28
[10,2,1,1] => 19
[10,1,1,1,1] => 10
[9,5] => 35
[9,4,1] => 30
[9,3,2] => 39
[9,3,1,1] => 24
[9,2,2,1] => 25
[9,2,1,1,1] => 17
[9,1,1,1,1,1] => 9
[8,6] => 33
[8,5,1] => 30
[8,4,2] => 44
[8,4,1,1] => 26
[8,3,3] => 40
[8,3,2,1] => 34
[8,3,1,1,1] => 21
[8,2,2,2] => 29
[8,2,2,1,1] => 22
[8,2,1,1,1,1] => 15
[8,1,1,1,1,1,1] => 8
[7,7] => 28
[7,6,1] => 27
[7,5,2] => 43
[7,5,1,1] => 25
[7,4,3] => 46
[7,4,2,1] => 37
[7,4,1,1,1] => 22
[7,3,3,1] => 34
[7,3,2,2] => 40
[7,3,2,1,1] => 29
[7,3,1,1,1,1] => 18
[7,2,2,2,1] => 25
[7,2,2,1,1,1] => 19
[7,2,1,1,1,1,1] => 13
[7,1,1,1,1,1,1,1] => 7
[6,6,2] => 36
[6,6,1,1] => 21
[6,5,3] => 43
[6,5,2,1] => 34
[6,5,1,1,1] => 20
[6,4,4] => 40
[6,4,3,1] => 37
[6,4,2,2] => 42
[6,4,2,1,1] => 30
[6,4,1,1,1,1] => 18
[6,3,3,2] => 41
[6,3,3,1,1] => 28
[6,3,2,2,1] => 33
[6,3,2,1,1,1] => 24
[6,3,1,1,1,1,1] => 15
[6,2,2,2,2] => 26
[6,2,2,2,1,1] => 21
[6,2,2,1,1,1,1] => 16
[6,2,1,1,1,1,1,1] => 11
[6,1,1,1,1,1,1,1,1] => 6
[5,5,4] => 34
[5,5,3,1] => 31
[5,5,2,2] => 35
[5,5,2,1,1] => 25
[5,5,1,1,1,1] => 15
[5,4,4,1] => 30
[5,4,3,2] => 42
[5,4,3,1,1] => 28
[5,4,2,2,1] => 32
[5,4,2,1,1,1] => 23
[5,4,1,1,1,1,1] => 14
[5,3,3,3] => 35
[5,3,3,2,1] => 32
[5,3,3,1,1,1] => 22
[5,3,2,2,2] => 33
[5,3,2,2,1,1] => 26
[5,3,2,1,1,1,1] => 19
[5,3,1,1,1,1,1,1] => 12
[5,2,2,2,2,1] => 21
[5,2,2,2,1,1,1] => 17
[5,2,2,1,1,1,1,1] => 13
[5,2,1,1,1,1,1,1,1] => 9
[5,1,1,1,1,1,1,1,1,1] => 5
[4,4,4,2] => 30
[4,4,4,1,1] => 20
[4,4,3,3] => 31
[4,4,3,2,1] => 28
[4,4,3,1,1,1] => 19
[4,4,2,2,2] => 28
[4,4,2,2,1,1] => 22
[4,4,2,1,1,1,1] => 16
[4,4,1,1,1,1,1,1] => 10
[4,3,3,3,1] => 25
[4,3,3,2,2] => 30
[4,3,3,2,1,1] => 23
[4,3,3,1,1,1,1] => 16
[4,3,2,2,2,1] => 24
[4,3,2,2,1,1,1] => 19
[4,3,2,1,1,1,1,1] => 14
[4,3,1,1,1,1,1,1,1] => 9
[4,2,2,2,2,2] => 19
[4,2,2,2,2,1,1] => 16
[4,2,2,2,1,1,1,1] => 13
[4,2,2,1,1,1,1,1,1] => 10
[4,2,1,1,1,1,1,1,1,1] => 7
[4,1,1,1,1,1,1,1,1,1,1] => 4
[3,3,3,3,2] => 20
[3,3,3,3,1,1] => 15
[3,3,3,2,2,1] => 18
[3,3,3,2,1,1,1] => 14
[3,3,3,1,1,1,1,1] => 10
[3,3,2,2,2,2] => 18
[3,3,2,2,2,1,1] => 15
[3,3,2,2,1,1,1,1] => 12
[3,3,2,1,1,1,1,1,1] => 9
[3,3,1,1,1,1,1,1,1,1] => 6
[3,2,2,2,2,2,1] => 13
[3,2,2,2,2,1,1,1] => 11
[3,2,2,2,1,1,1,1,1] => 9
[3,2,2,1,1,1,1,1,1,1] => 7
[3,2,1,1,1,1,1,1,1,1,1] => 5
[3,1,1,1,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,2,2] => 8
[2,2,2,2,2,2,1,1] => 7
[2,2,2,2,2,1,1,1,1] => 6
[2,2,2,2,1,1,1,1,1,1] => 5
[2,2,2,1,1,1,1,1,1,1,1] => 4
[2,2,1,1,1,1,1,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[15] => 15
[14,1] => 14
[13,2] => 25
[13,1,1] => 13
[12,3] => 33
[12,2,1] => 23
[12,1,1,1] => 12
[11,4] => 38
[11,3,1] => 30
[11,2,2] => 31
[11,2,1,1] => 21
[11,1,1,1,1] => 11
[10,5] => 40
[10,4,1] => 34
[10,3,2] => 44
[10,3,1,1] => 27
[10,2,2,1] => 28
[10,2,1,1,1] => 19
[10,1,1,1,1,1] => 10
[9,6] => 39
[9,5,1] => 35
[9,4,2] => 51
[9,4,1,1] => 30
[9,3,3] => 46
[9,3,2,1] => 39
[9,3,1,1,1] => 24
[9,2,2,2] => 33
[9,2,2,1,1] => 25
[9,2,1,1,1,1] => 17
[9,1,1,1,1,1,1] => 9
[8,7] => 35
[8,6,1] => 33
[8,5,2] => 52
[8,5,1,1] => 30
[8,4,3] => 55
[8,4,2,1] => 44
[8,4,1,1,1] => 26
[8,3,3,1] => 40
[8,3,2,2] => 47
[8,3,2,1,1] => 34
[8,3,1,1,1,1] => 21
[8,2,2,2,1] => 29
[8,2,2,1,1,1] => 22
[8,2,1,1,1,1,1] => 15
[8,1,1,1,1,1,1,1] => 8
[7,7,1] => 28
[7,6,2] => 47
[7,6,1,1] => 27
[7,5,3] => 55
[7,5,2,1] => 43
[7,5,1,1,1] => 25
[7,4,4] => 50
[7,4,3,1] => 46
[7,4,2,2] => 52
[7,4,2,1,1] => 37
[7,4,1,1,1,1] => 22
[7,3,3,2] => 50
[7,3,3,1,1] => 34
[7,3,2,2,1] => 40
[7,3,2,1,1,1] => 29
[7,3,1,1,1,1,1] => 18
[7,2,2,2,2] => 31
[7,2,2,2,1,1] => 25
[7,2,2,1,1,1,1] => 19
[7,2,1,1,1,1,1,1] => 13
[7,1,1,1,1,1,1,1,1] => 7
[6,6,3] => 46
[6,6,2,1] => 36
[6,6,1,1,1] => 21
[6,5,4] => 48
[6,5,3,1] => 43
[6,5,2,2] => 48
[6,5,2,1,1] => 34
[6,5,1,1,1,1] => 20
[6,4,4,1] => 40
[6,4,3,2] => 56
[6,4,3,1,1] => 37
[6,4,2,2,1] => 42
[6,4,2,1,1,1] => 30
[6,4,1,1,1,1,1] => 18
[6,3,3,3] => 45
[6,3,3,2,1] => 41
[6,3,3,1,1,1] => 28
[6,3,2,2,2] => 42
[6,3,2,2,1,1] => 33
[6,3,2,1,1,1,1] => 24
[6,3,1,1,1,1,1,1] => 15
[6,2,2,2,2,1] => 26
[6,2,2,2,1,1,1] => 21
[6,2,2,1,1,1,1,1] => 16
[6,2,1,1,1,1,1,1,1] => 11
[6,1,1,1,1,1,1,1,1,1] => 6
[5,5,5] => 35
[5,5,4,1] => 34
[5,5,3,2] => 47
[5,5,3,1,1] => 31
[5,5,2,2,1] => 35
[5,5,2,1,1,1] => 25
[5,5,1,1,1,1,1] => 15
[5,4,4,2] => 46
[5,4,4,1,1] => 30
[5,4,3,3] => 47
[5,4,3,2,1] => 42
[5,4,3,1,1,1] => 28
[5,4,2,2,2] => 41
[5,4,2,2,1,1] => 32
[5,4,2,1,1,1,1] => 23
[5,4,1,1,1,1,1,1] => 14
[5,3,3,3,1] => 35
[5,3,3,2,2] => 42
[5,3,3,2,1,1] => 32
[5,3,3,1,1,1,1] => 22
[5,3,2,2,2,1] => 33
[5,3,2,2,1,1,1] => 26
[5,3,2,1,1,1,1,1] => 19
[5,3,1,1,1,1,1,1,1] => 12
[5,2,2,2,2,2] => 25
[5,2,2,2,2,1,1] => 21
[5,2,2,2,1,1,1,1] => 17
[5,2,2,1,1,1,1,1,1] => 13
[5,2,1,1,1,1,1,1,1,1] => 9
[5,1,1,1,1,1,1,1,1,1,1] => 5
[4,4,4,3] => 34
[4,4,4,2,1] => 30
[4,4,4,1,1,1] => 20
[4,4,3,3,1] => 31
[4,4,3,2,2] => 37
[4,4,3,2,1,1] => 28
[4,4,3,1,1,1,1] => 19
[4,4,2,2,2,1] => 28
[4,4,2,2,1,1,1] => 22
[4,4,2,1,1,1,1,1] => 16
[4,4,1,1,1,1,1,1,1] => 10
[4,3,3,3,2] => 34
[4,3,3,3,1,1] => 25
[4,3,3,2,2,1] => 30
[4,3,3,2,1,1,1] => 23
[4,3,3,1,1,1,1,1] => 16
[4,3,2,2,2,2] => 29
[4,3,2,2,2,1,1] => 24
[4,3,2,2,1,1,1,1] => 19
[4,3,2,1,1,1,1,1,1] => 14
[4,3,1,1,1,1,1,1,1,1] => 9
[4,2,2,2,2,2,1] => 19
[4,2,2,2,2,1,1,1] => 16
[4,2,2,2,1,1,1,1,1] => 13
[4,2,2,1,1,1,1,1,1,1] => 10
[4,2,1,1,1,1,1,1,1,1,1] => 7
[4,1,1,1,1,1,1,1,1,1,1,1] => 4
[3,3,3,3,3] => 21
[3,3,3,3,2,1] => 20
[3,3,3,3,1,1,1] => 15
[3,3,3,2,2,2] => 22
[3,3,3,2,2,1,1] => 18
[3,3,3,2,1,1,1,1] => 14
[3,3,3,1,1,1,1,1,1] => 10
[3,3,2,2,2,2,1] => 18
[3,3,2,2,2,1,1,1] => 15
[3,3,2,2,1,1,1,1,1] => 12
[3,3,2,1,1,1,1,1,1,1] => 9
[3,3,1,1,1,1,1,1,1,1,1] => 6
[3,2,2,2,2,2,2] => 15
[3,2,2,2,2,2,1,1] => 13
[3,2,2,2,2,1,1,1,1] => 11
[3,2,2,2,1,1,1,1,1,1] => 9
[3,2,2,1,1,1,1,1,1,1,1] => 7
[3,2,1,1,1,1,1,1,1,1,1,1] => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,2,2,1] => 8
[2,2,2,2,2,2,1,1,1] => 7
[2,2,2,2,2,1,1,1,1,1] => 6
[2,2,2,2,1,1,1,1,1,1,1] => 5
[2,2,2,1,1,1,1,1,1,1,1,1] => 4
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[16] => 16
[15,1] => 15
[14,2] => 27
[14,1,1] => 14
[13,3] => 36
[13,2,1] => 25
[13,1,1,1] => 13
[12,4] => 42
[12,3,1] => 33
[12,2,2] => 34
[12,2,1,1] => 23
[12,1,1,1,1] => 12
[11,5] => 45
[11,4,1] => 38
[11,3,2] => 49
[11,3,1,1] => 30
[11,2,2,1] => 31
[11,2,1,1,1] => 21
[11,1,1,1,1,1] => 11
[10,6] => 45
[10,5,1] => 40
[10,4,2] => 58
[10,4,1,1] => 34
[10,3,3] => 52
[10,3,2,1] => 44
[10,3,1,1,1] => 27
[10,2,2,2] => 37
[10,2,2,1,1] => 28
[10,2,1,1,1,1] => 19
[10,1,1,1,1,1,1] => 10
[9,7] => 42
[9,6,1] => 39
[9,5,2] => 61
[9,5,1,1] => 35
[9,4,3] => 64
[9,4,2,1] => 51
[9,4,1,1,1] => 30
[9,3,3,1] => 46
[9,3,2,2] => 54
[9,3,2,1,1] => 39
[9,3,1,1,1,1] => 24
[9,2,2,2,1] => 33
[9,2,2,1,1,1] => 25
[9,2,1,1,1,1,1] => 17
[9,1,1,1,1,1,1,1] => 9
[8,8] => 36
[8,7,1] => 35
[8,6,2] => 58
[8,6,1,1] => 33
[8,5,3] => 67
[8,5,2,1] => 52
[8,5,1,1,1] => 30
[8,4,4] => 60
[8,4,3,1] => 55
[8,4,2,2] => 62
[8,4,2,1,1] => 44
[8,4,1,1,1,1] => 26
[8,3,3,2] => 59
[8,3,3,1,1] => 40
[8,3,2,2,1] => 47
[8,3,2,1,1,1] => 34
[8,3,1,1,1,1,1] => 21
[8,2,2,2,2] => 36
[8,2,2,2,1,1] => 29
[8,2,2,1,1,1,1] => 22
[8,2,1,1,1,1,1,1] => 15
[8,1,1,1,1,1,1,1,1] => 8
[7,7,2] => 49
[7,7,1,1] => 28
[7,6,3] => 61
[7,6,2,1] => 47
[7,6,1,1,1] => 27
[7,5,4] => 62
[7,5,3,1] => 55
[7,5,2,2] => 61
[7,5,2,1,1] => 43
[7,5,1,1,1,1] => 25
[7,4,4,1] => 50
[7,4,3,2] => 70
[7,4,3,1,1] => 46
[7,4,2,2,1] => 52
[7,4,2,1,1,1] => 37
[7,4,1,1,1,1,1] => 22
[7,3,3,3] => 55
[7,3,3,2,1] => 50
[7,3,3,1,1,1] => 34
[7,3,2,2,2] => 51
[7,3,2,2,1,1] => 40
[7,3,2,1,1,1,1] => 29
[7,3,1,1,1,1,1,1] => 18
[7,2,2,2,2,1] => 31
[7,2,2,2,1,1,1] => 25
[7,2,2,1,1,1,1,1] => 19
[7,2,1,1,1,1,1,1,1] => 13
[7,1,1,1,1,1,1,1,1,1] => 7
[6,6,4] => 52
[6,6,3,1] => 46
[6,6,2,2] => 51
[6,6,2,1,1] => 36
[6,6,1,1,1,1] => 21
[6,5,5] => 50
[6,5,4,1] => 48
[6,5,3,2] => 66
[6,5,3,1,1] => 43
[6,5,2,2,1] => 48
[6,5,2,1,1,1] => 34
[6,5,1,1,1,1,1] => 20
[6,4,4,2] => 62
[6,4,4,1,1] => 40
[6,4,3,3] => 63
[6,4,3,2,1] => 56
[6,4,3,1,1,1] => 37
[6,4,2,2,2] => 54
[6,4,2,2,1,1] => 42
[6,4,2,1,1,1,1] => 30
[6,4,1,1,1,1,1,1] => 18
[6,3,3,3,1] => 45
[6,3,3,2,2] => 54
[6,3,3,2,1,1] => 41
[6,3,3,1,1,1,1] => 28
[6,3,2,2,2,1] => 42
[6,3,2,2,1,1,1] => 33
[6,3,2,1,1,1,1,1] => 24
[6,3,1,1,1,1,1,1,1] => 15
[6,2,2,2,2,2] => 31
[6,2,2,2,2,1,1] => 26
[6,2,2,2,1,1,1,1] => 21
[6,2,2,1,1,1,1,1,1] => 16
[6,2,1,1,1,1,1,1,1,1] => 11
[6,1,1,1,1,1,1,1,1,1,1] => 6
[5,5,5,1] => 35
[5,5,4,2] => 53
[5,5,4,1,1] => 34
[5,5,3,3] => 53
[5,5,3,2,1] => 47
[5,5,3,1,1,1] => 31
[5,5,2,2,2] => 45
[5,5,2,2,1,1] => 35
[5,5,2,1,1,1,1] => 25
[5,5,1,1,1,1,1,1] => 15
[5,4,4,3] => 53
[5,4,4,2,1] => 46
[5,4,4,1,1,1] => 30
[5,4,3,3,1] => 47
[5,4,3,2,2] => 56
[5,4,3,2,1,1] => 42
[5,4,3,1,1,1,1] => 28
[5,4,2,2,2,1] => 41
[5,4,2,2,1,1,1] => 32
[5,4,2,1,1,1,1,1] => 23
[5,4,1,1,1,1,1,1,1] => 14
[5,3,3,3,2] => 48
[5,3,3,3,1,1] => 35
[5,3,3,2,2,1] => 42
[5,3,3,2,1,1,1] => 32
[5,3,3,1,1,1,1,1] => 22
[5,3,2,2,2,2] => 40
[5,3,2,2,2,1,1] => 33
[5,3,2,2,1,1,1,1] => 26
[5,3,2,1,1,1,1,1,1] => 19
[5,3,1,1,1,1,1,1,1,1] => 12
[5,2,2,2,2,2,1] => 25
[5,2,2,2,2,1,1,1] => 21
[5,2,2,2,1,1,1,1,1] => 17
[5,2,2,1,1,1,1,1,1,1] => 13
[5,2,1,1,1,1,1,1,1,1,1] => 9
[5,1,1,1,1,1,1,1,1,1,1,1] => 5
[4,4,4,4] => 35
[4,4,4,3,1] => 34
[4,4,4,2,2] => 40
[4,4,4,2,1,1] => 30
[4,4,4,1,1,1,1] => 20
[4,4,3,3,2] => 43
[4,4,3,3,1,1] => 31
[4,4,3,2,2,1] => 37
[4,4,3,2,1,1,1] => 28
[4,4,3,1,1,1,1,1] => 19
[4,4,2,2,2,2] => 34
[4,4,2,2,2,1,1] => 28
[4,4,2,2,1,1,1,1] => 22
[4,4,2,1,1,1,1,1,1] => 16
[4,4,1,1,1,1,1,1,1,1] => 10
[4,3,3,3,3] => 36
[4,3,3,3,2,1] => 34
[4,3,3,3,1,1,1] => 25
[4,3,3,2,2,2] => 37
[4,3,3,2,2,1,1] => 30
[4,3,3,2,1,1,1,1] => 23
[4,3,3,1,1,1,1,1,1] => 16
[4,3,2,2,2,2,1] => 29
[4,3,2,2,2,1,1,1] => 24
[4,3,2,2,1,1,1,1,1] => 19
[4,3,2,1,1,1,1,1,1,1] => 14
[4,3,1,1,1,1,1,1,1,1,1] => 9
[4,2,2,2,2,2,2] => 22
[4,2,2,2,2,2,1,1] => 19
[4,2,2,2,2,1,1,1,1] => 16
[4,2,2,2,1,1,1,1,1,1] => 13
[4,2,2,1,1,1,1,1,1,1,1] => 10
[4,2,1,1,1,1,1,1,1,1,1,1] => 7
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 4
[3,3,3,3,3,1] => 21
[3,3,3,3,2,2] => 25
[3,3,3,3,2,1,1] => 20
[3,3,3,3,1,1,1,1] => 15
[3,3,3,2,2,2,1] => 22
[3,3,3,2,2,1,1,1] => 18
[3,3,3,2,1,1,1,1,1] => 14
[3,3,3,1,1,1,1,1,1,1] => 10
[3,3,2,2,2,2,2] => 21
[3,3,2,2,2,2,1,1] => 18
[3,3,2,2,2,1,1,1,1] => 15
[3,3,2,2,1,1,1,1,1,1] => 12
[3,3,2,1,1,1,1,1,1,1,1] => 9
[3,3,1,1,1,1,1,1,1,1,1,1] => 6
[3,2,2,2,2,2,2,1] => 15
[3,2,2,2,2,2,1,1,1] => 13
[3,2,2,2,2,1,1,1,1,1] => 11
[3,2,2,2,1,1,1,1,1,1,1] => 9
[3,2,2,1,1,1,1,1,1,1,1,1] => 7
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,2,2,2] => 9
[2,2,2,2,2,2,2,1,1] => 8
[2,2,2,2,2,2,1,1,1,1] => 7
[2,2,2,2,2,1,1,1,1,1,1] => 6
[2,2,2,2,1,1,1,1,1,1,1,1] => 5
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 4
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[17] => 17
[16,1] => 16
[15,2] => 29
[15,1,1] => 15
[14,3] => 39
[14,2,1] => 27
[14,1,1,1] => 14
[13,4] => 46
[13,3,1] => 36
[13,2,2] => 37
[13,2,1,1] => 25
[13,1,1,1,1] => 13
[12,5] => 50
[12,4,1] => 42
[12,3,2] => 54
[12,3,1,1] => 33
[12,2,2,1] => 34
[12,2,1,1,1] => 23
[12,1,1,1,1,1] => 12
[11,6] => 51
[11,5,1] => 45
[11,4,2] => 65
[11,4,1,1] => 38
[11,3,3] => 58
[11,3,2,1] => 49
[11,3,1,1,1] => 30
[11,2,2,2] => 41
[11,2,2,1,1] => 31
[11,2,1,1,1,1] => 21
[11,1,1,1,1,1,1] => 11
[10,7] => 49
[10,6,1] => 45
[10,5,2] => 70
[10,5,1,1] => 40
[10,4,3] => 73
[10,4,2,1] => 58
[10,4,1,1,1] => 34
[10,3,3,1] => 52
[10,3,2,2] => 61
[10,3,2,1,1] => 44
[10,3,1,1,1,1] => 27
[10,2,2,2,1] => 37
[10,2,2,1,1,1] => 28
[10,2,1,1,1,1,1] => 19
[10,1,1,1,1,1,1,1] => 10
[9,8] => 44
[9,7,1] => 42
[9,6,2] => 69
[9,6,1,1] => 39
[9,5,3] => 79
[9,5,2,1] => 61
[9,5,1,1,1] => 35
[9,4,4] => 70
[9,4,3,1] => 64
[9,4,2,2] => 72
[9,4,2,1,1] => 51
[9,4,1,1,1,1] => 30
[9,3,3,2] => 68
[9,3,3,1,1] => 46
[9,3,2,2,1] => 54
[9,3,2,1,1,1] => 39
[9,3,1,1,1,1,1] => 24
[9,2,2,2,2] => 41
[9,2,2,2,1,1] => 33
[9,2,2,1,1,1,1] => 25
[9,2,1,1,1,1,1,1] => 17
[9,1,1,1,1,1,1,1,1] => 9
[8,8,1] => 36
[8,7,2] => 62
[8,7,1,1] => 35
[8,6,3] => 76
[8,6,2,1] => 58
[8,6,1,1,1] => 33
[8,5,4] => 76
[8,5,3,1] => 67
[8,5,2,2] => 74
[8,5,2,1,1] => 52
[8,5,1,1,1,1] => 30
[8,4,4,1] => 60
[8,4,3,2] => 84
[8,4,3,1,1] => 55
[8,4,2,2,1] => 62
[8,4,2,1,1,1] => 44
[8,4,1,1,1,1,1] => 26
[8,3,3,3] => 65
[8,3,3,2,1] => 59
[8,3,3,1,1,1] => 40
[8,3,2,2,2] => 60
[8,3,2,2,1,1] => 47
[8,3,2,1,1,1,1] => 34
[8,3,1,1,1,1,1,1] => 21
[8,2,2,2,2,1] => 36
[8,2,2,2,1,1,1] => 29
[8,2,2,1,1,1,1,1] => 22
[8,2,1,1,1,1,1,1,1] => 15
[8,1,1,1,1,1,1,1,1,1] => 8
[7,7,3] => 64
[7,7,2,1] => 49
[7,7,1,1,1] => 28
[7,6,4] => 70
[7,6,3,1] => 61
[7,6,2,2] => 67
[7,6,2,1,1] => 47
[7,6,1,1,1,1] => 27
[7,5,5] => 65
[7,5,4,1] => 62
[7,5,3,2] => 85
[7,5,3,1,1] => 55
[7,5,2,2,1] => 61
[7,5,2,1,1,1] => 43
[7,5,1,1,1,1,1] => 25
[7,4,4,2] => 78
[7,4,4,1,1] => 50
[7,4,3,3] => 79
[7,4,3,2,1] => 70
[7,4,3,1,1,1] => 46
[7,4,2,2,2] => 67
[7,4,2,2,1,1] => 52
[7,4,2,1,1,1,1] => 37
[7,4,1,1,1,1,1,1] => 22
[7,3,3,3,1] => 55
[7,3,3,2,2] => 66
[7,3,3,2,1,1] => 50
[7,3,3,1,1,1,1] => 34
[7,3,2,2,2,1] => 51
[7,3,2,2,1,1,1] => 40
[7,3,2,1,1,1,1,1] => 29
[7,3,1,1,1,1,1,1,1] => 18
[7,2,2,2,2,2] => 37
[7,2,2,2,2,1,1] => 31
[7,2,2,2,1,1,1,1] => 25
[7,2,2,1,1,1,1,1,1] => 19
[7,2,1,1,1,1,1,1,1,1] => 13
[7,1,1,1,1,1,1,1,1,1,1] => 7
[6,6,5] => 55
[6,6,4,1] => 52
[6,6,3,2] => 71
[6,6,3,1,1] => 46
[6,6,2,2,1] => 51
[6,6,2,1,1,1] => 36
[6,6,1,1,1,1,1] => 21
[6,5,5,1] => 50
[6,5,4,2] => 76
[6,5,4,1,1] => 48
[6,5,3,3] => 75
[6,5,3,2,1] => 66
[6,5,3,1,1,1] => 43
[6,5,2,2,2] => 62
[6,5,2,2,1,1] => 48
[6,5,2,1,1,1,1] => 34
[6,5,1,1,1,1,1,1] => 20
[6,4,4,3] => 72
[6,4,4,2,1] => 62
[6,4,4,1,1,1] => 40
[6,4,3,3,1] => 63
[6,4,3,2,2] => 75
[6,4,3,2,1,1] => 56
[6,4,3,1,1,1,1] => 37
[6,4,2,2,2,1] => 54
[6,4,2,2,1,1,1] => 42
[6,4,2,1,1,1,1,1] => 30
[6,4,1,1,1,1,1,1,1] => 18
[6,3,3,3,2] => 62
[6,3,3,3,1,1] => 45
[6,3,3,2,2,1] => 54
[6,3,3,2,1,1,1] => 41
[6,3,3,1,1,1,1,1] => 28
[6,3,2,2,2,2] => 51
[6,3,2,2,2,1,1] => 42
[6,3,2,2,1,1,1,1] => 33
[6,3,2,1,1,1,1,1,1] => 24
[6,3,1,1,1,1,1,1,1,1] => 15
[6,2,2,2,2,2,1] => 31
[6,2,2,2,2,1,1,1] => 26
[6,2,2,2,1,1,1,1,1] => 21
[6,2,2,1,1,1,1,1,1,1] => 16
[6,2,1,1,1,1,1,1,1,1,1] => 11
[6,1,1,1,1,1,1,1,1,1,1,1] => 6
[5,5,5,2] => 55
[5,5,5,1,1] => 35
[5,5,4,3] => 62
[5,5,4,2,1] => 53
[5,5,4,1,1,1] => 34
[5,5,3,3,1] => 53
[5,5,3,2,2] => 63
[5,5,3,2,1,1] => 47
[5,5,3,1,1,1,1] => 31
[5,5,2,2,2,1] => 45
[5,5,2,2,1,1,1] => 35
[5,5,2,1,1,1,1,1] => 25
[5,5,1,1,1,1,1,1,1] => 15
[5,4,4,4] => 55
[5,4,4,3,1] => 53
[5,4,4,2,2] => 62
[5,4,4,2,1,1] => 46
[5,4,4,1,1,1,1] => 30
[5,4,3,3,2] => 66
[5,4,3,3,1,1] => 47
[5,4,3,2,2,1] => 56
[5,4,3,2,1,1,1] => 42
[5,4,3,1,1,1,1,1] => 28
[5,4,2,2,2,2] => 50
[5,4,2,2,2,1,1] => 41
[5,4,2,2,1,1,1,1] => 32
[5,4,2,1,1,1,1,1,1] => 23
[5,4,1,1,1,1,1,1,1,1] => 14
[5,3,3,3,3] => 51
[5,3,3,3,2,1] => 48
[5,3,3,3,1,1,1] => 35
[5,3,3,2,2,2] => 52
[5,3,3,2,2,1,1] => 42
[5,3,3,2,1,1,1,1] => 32
[5,3,3,1,1,1,1,1,1] => 22
[5,3,2,2,2,2,1] => 40
[5,3,2,2,2,1,1,1] => 33
[5,3,2,2,1,1,1,1,1] => 26
[5,3,2,1,1,1,1,1,1,1] => 19
[5,3,1,1,1,1,1,1,1,1,1] => 12
[5,2,2,2,2,2,2] => 29
[5,2,2,2,2,2,1,1] => 25
[5,2,2,2,2,1,1,1,1] => 21
[5,2,2,2,1,1,1,1,1,1] => 17
[5,2,2,1,1,1,1,1,1,1,1] => 13
[5,2,1,1,1,1,1,1,1,1,1,1] => 9
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 5
[4,4,4,4,1] => 35
[4,4,4,3,2] => 48
[4,4,4,3,1,1] => 34
[4,4,4,2,2,1] => 40
[4,4,4,2,1,1,1] => 30
[4,4,4,1,1,1,1,1] => 20
[4,4,3,3,3] => 46
[4,4,3,3,2,1] => 43
[4,4,3,3,1,1,1] => 31
[4,4,3,2,2,2] => 46
[4,4,3,2,2,1,1] => 37
[4,4,3,2,1,1,1,1] => 28
[4,4,3,1,1,1,1,1,1] => 19
[4,4,2,2,2,2,1] => 34
[4,4,2,2,2,1,1,1] => 28
[4,4,2,2,1,1,1,1,1] => 22
[4,4,2,1,1,1,1,1,1,1] => 16
[4,4,1,1,1,1,1,1,1,1,1] => 10
[4,3,3,3,3,1] => 36
[4,3,3,3,2,2] => 43
[4,3,3,3,2,1,1] => 34
[4,3,3,3,1,1,1,1] => 25
[4,3,3,2,2,2,1] => 37
[4,3,3,2,2,1,1,1] => 30
[4,3,3,2,1,1,1,1,1] => 23
[4,3,3,1,1,1,1,1,1,1] => 16
[4,3,2,2,2,2,2] => 34
[4,3,2,2,2,2,1,1] => 29
[4,3,2,2,2,1,1,1,1] => 24
[4,3,2,2,1,1,1,1,1,1] => 19
[4,3,2,1,1,1,1,1,1,1,1] => 14
[4,3,1,1,1,1,1,1,1,1,1,1] => 9
[4,2,2,2,2,2,2,1] => 22
[4,2,2,2,2,2,1,1,1] => 19
[4,2,2,2,2,1,1,1,1,1] => 16
[4,2,2,2,1,1,1,1,1,1,1] => 13
[4,2,2,1,1,1,1,1,1,1,1,1] => 10
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 7
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 4
[3,3,3,3,3,2] => 27
[3,3,3,3,3,1,1] => 21
[3,3,3,3,2,2,1] => 25
[3,3,3,3,2,1,1,1] => 20
[3,3,3,3,1,1,1,1,1] => 15
[3,3,3,2,2,2,2] => 26
[3,3,3,2,2,2,1,1] => 22
[3,3,3,2,2,1,1,1,1] => 18
[3,3,3,2,1,1,1,1,1,1] => 14
[3,3,3,1,1,1,1,1,1,1,1] => 10
[3,3,2,2,2,2,2,1] => 21
[3,3,2,2,2,2,1,1,1] => 18
[3,3,2,2,2,1,1,1,1,1] => 15
[3,3,2,2,1,1,1,1,1,1,1] => 12
[3,3,2,1,1,1,1,1,1,1,1,1] => 9
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 6
[3,2,2,2,2,2,2,2] => 17
[3,2,2,2,2,2,2,1,1] => 15
[3,2,2,2,2,2,1,1,1,1] => 13
[3,2,2,2,2,1,1,1,1,1,1] => 11
[3,2,2,2,1,1,1,1,1,1,1,1] => 9
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 7
-----------------------------------------------------------------------------
Created: May 11, 2019 at 18:25 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: May 11, 2019 at 18:25 by Martin Rubey