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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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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001541
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The Gini index of an integer partition.
As discussed in [1], this statistic is equal to [[St000567]] applied to the conjugate partition.
-----------------------------------------------------------------------------
References: [1] Kopitzke, G. The Gini Index of an Integer Partition [[arXiv:2005.04284]]
-----------------------------------------------------------------------------
Code:
def statistic(L):
L = L.conjugate()
n = sum(L)
return binomial(n+1,2) - sum(binomial(l+1,2) for l in L)
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[2] => 1
[1,1] => 0
[3] => 3
[2,1] => 2
[1,1,1] => 0
[4] => 6
[3,1] => 5
[2,2] => 4
[2,1,1] => 3
[1,1,1,1] => 0
[5] => 10
[4,1] => 9
[3,2] => 8
[3,1,1] => 7
[2,2,1] => 6
[2,1,1,1] => 4
[1,1,1,1,1] => 0
[6] => 15
[5,1] => 14
[4,2] => 13
[4,1,1] => 12
[3,3] => 12
[3,2,1] => 11
[3,1,1,1] => 9
[2,2,2] => 9
[2,2,1,1] => 8
[2,1,1,1,1] => 5
[1,1,1,1,1,1] => 0
[7] => 21
[6,1] => 20
[5,2] => 19
[5,1,1] => 18
[4,3] => 18
[4,2,1] => 17
[4,1,1,1] => 15
[3,3,1] => 16
[3,2,2] => 15
[3,2,1,1] => 14
[3,1,1,1,1] => 11
[2,2,2,1] => 12
[2,2,1,1,1] => 10
[2,1,1,1,1,1] => 6
[1,1,1,1,1,1,1] => 0
[8] => 28
[7,1] => 27
[6,2] => 26
[6,1,1] => 25
[5,3] => 25
[5,2,1] => 24
[5,1,1,1] => 22
[4,4] => 24
[4,3,1] => 23
[4,2,2] => 22
[4,2,1,1] => 21
[4,1,1,1,1] => 18
[3,3,2] => 21
[3,3,1,1] => 20
[3,2,2,1] => 19
[3,2,1,1,1] => 17
[3,1,1,1,1,1] => 13
[2,2,2,2] => 16
[2,2,2,1,1] => 15
[2,2,1,1,1,1] => 12
[2,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,1] => 0
[9] => 36
[8,1] => 35
[7,2] => 34
[7,1,1] => 33
[6,3] => 33
[6,2,1] => 32
[6,1,1,1] => 30
[5,4] => 32
[5,3,1] => 31
[5,2,2] => 30
[5,2,1,1] => 29
[5,1,1,1,1] => 26
[4,4,1] => 30
[4,3,2] => 29
[4,3,1,1] => 28
[4,2,2,1] => 27
[4,2,1,1,1] => 25
[4,1,1,1,1,1] => 21
[3,3,3] => 27
[3,3,2,1] => 26
[3,3,1,1,1] => 24
[3,2,2,2] => 24
[3,2,2,1,1] => 23
[3,2,1,1,1,1] => 20
[3,1,1,1,1,1,1] => 15
[2,2,2,2,1] => 20
[2,2,2,1,1,1] => 18
[2,2,1,1,1,1,1] => 14
[2,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1,1] => 0
[10] => 45
[9,1] => 44
[8,2] => 43
[8,1,1] => 42
[7,3] => 42
[7,2,1] => 41
[7,1,1,1] => 39
[6,4] => 41
[6,3,1] => 40
[6,2,2] => 39
[6,2,1,1] => 38
[6,1,1,1,1] => 35
[5,5] => 40
[5,4,1] => 39
[5,3,2] => 38
[5,3,1,1] => 37
[5,2,2,1] => 36
[5,2,1,1,1] => 34
[5,1,1,1,1,1] => 30
[4,4,2] => 37
[4,4,1,1] => 36
[4,3,3] => 36
[4,3,2,1] => 35
[4,3,1,1,1] => 33
[4,2,2,2] => 33
[4,2,2,1,1] => 32
[4,2,1,1,1,1] => 29
[4,1,1,1,1,1,1] => 24
[3,3,3,1] => 33
[3,3,2,2] => 32
[3,3,2,1,1] => 31
[3,3,1,1,1,1] => 28
[3,2,2,2,1] => 29
[3,2,2,1,1,1] => 27
[3,2,1,1,1,1,1] => 23
[3,1,1,1,1,1,1,1] => 17
[2,2,2,2,2] => 25
[2,2,2,2,1,1] => 24
[2,2,2,1,1,1,1] => 21
[2,2,1,1,1,1,1,1] => 16
[2,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,1,1,1] => 0
[11] => 55
[10,1] => 54
[9,2] => 53
[9,1,1] => 52
[8,3] => 52
[8,2,1] => 51
[8,1,1,1] => 49
[7,4] => 51
[7,3,1] => 50
[7,2,2] => 49
[7,2,1,1] => 48
[7,1,1,1,1] => 45
[6,5] => 50
[6,4,1] => 49
[6,3,2] => 48
[6,3,1,1] => 47
[6,2,2,1] => 46
[6,2,1,1,1] => 44
[6,1,1,1,1,1] => 40
[5,5,1] => 48
[5,4,2] => 47
[5,4,1,1] => 46
[5,3,3] => 46
[5,3,2,1] => 45
[5,3,1,1,1] => 43
[5,2,2,2] => 43
[5,2,2,1,1] => 42
[5,2,1,1,1,1] => 39
[5,1,1,1,1,1,1] => 34
[4,4,3] => 45
[4,4,2,1] => 44
[4,4,1,1,1] => 42
[4,3,3,1] => 43
[4,3,2,2] => 42
[4,3,2,1,1] => 41
[4,3,1,1,1,1] => 38
[4,2,2,2,1] => 39
[4,2,2,1,1,1] => 37
[4,2,1,1,1,1,1] => 33
[4,1,1,1,1,1,1,1] => 27
[3,3,3,2] => 40
[3,3,3,1,1] => 39
[3,3,2,2,1] => 38
[3,3,2,1,1,1] => 36
[3,3,1,1,1,1,1] => 32
[3,2,2,2,2] => 35
[3,2,2,2,1,1] => 34
[3,2,2,1,1,1,1] => 31
[3,2,1,1,1,1,1,1] => 26
[3,1,1,1,1,1,1,1,1] => 19
[2,2,2,2,2,1] => 30
[2,2,2,2,1,1,1] => 28
[2,2,2,1,1,1,1,1] => 24
[2,2,1,1,1,1,1,1,1] => 18
[2,1,1,1,1,1,1,1,1,1] => 10
[1,1,1,1,1,1,1,1,1,1,1] => 0
[12] => 66
[11,1] => 65
[10,2] => 64
[10,1,1] => 63
[9,3] => 63
[9,2,1] => 62
[9,1,1,1] => 60
[8,4] => 62
[8,3,1] => 61
[8,2,2] => 60
[8,2,1,1] => 59
[8,1,1,1,1] => 56
[7,5] => 61
[7,4,1] => 60
[7,3,2] => 59
[7,3,1,1] => 58
[7,2,2,1] => 57
[7,2,1,1,1] => 55
[7,1,1,1,1,1] => 51
[6,6] => 60
[6,5,1] => 59
[6,4,2] => 58
[6,4,1,1] => 57
[6,3,3] => 57
[6,3,2,1] => 56
[6,3,1,1,1] => 54
[6,2,2,2] => 54
[6,2,2,1,1] => 53
[6,2,1,1,1,1] => 50
[6,1,1,1,1,1,1] => 45
[5,5,2] => 57
[5,5,1,1] => 56
[5,4,3] => 56
[5,4,2,1] => 55
[5,4,1,1,1] => 53
[5,3,3,1] => 54
[5,3,2,2] => 53
[5,3,2,1,1] => 52
[5,3,1,1,1,1] => 49
[5,2,2,2,1] => 50
[5,2,2,1,1,1] => 48
[5,2,1,1,1,1,1] => 44
[5,1,1,1,1,1,1,1] => 38
[4,4,4] => 54
[4,4,3,1] => 53
[4,4,2,2] => 52
[4,4,2,1,1] => 51
[4,4,1,1,1,1] => 48
[4,3,3,2] => 51
[4,3,3,1,1] => 50
[4,3,2,2,1] => 49
[4,3,2,1,1,1] => 47
[4,3,1,1,1,1,1] => 43
[4,2,2,2,2] => 46
[4,2,2,2,1,1] => 45
[4,2,2,1,1,1,1] => 42
[4,2,1,1,1,1,1,1] => 37
[4,1,1,1,1,1,1,1,1] => 30
[3,3,3,3] => 48
[3,3,3,2,1] => 47
[3,3,3,1,1,1] => 45
[3,3,2,2,2] => 45
[3,3,2,2,1,1] => 44
[3,3,2,1,1,1,1] => 41
[3,3,1,1,1,1,1,1] => 36
[3,2,2,2,2,1] => 41
[3,2,2,2,1,1,1] => 39
[3,2,2,1,1,1,1,1] => 35
[3,2,1,1,1,1,1,1,1] => 29
[3,1,1,1,1,1,1,1,1,1] => 21
[2,2,2,2,2,2] => 36
[2,2,2,2,2,1,1] => 35
[2,2,2,2,1,1,1,1] => 32
[2,2,2,1,1,1,1,1,1] => 27
[2,2,1,1,1,1,1,1,1,1] => 20
[2,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[13] => 78
[12,1] => 77
[11,2] => 76
[11,1,1] => 75
[10,3] => 75
[10,2,1] => 74
[10,1,1,1] => 72
[9,4] => 74
[9,3,1] => 73
[9,2,2] => 72
[9,2,1,1] => 71
[9,1,1,1,1] => 68
[8,5] => 73
[8,4,1] => 72
[8,3,2] => 71
[8,3,1,1] => 70
[8,2,2,1] => 69
[8,2,1,1,1] => 67
[8,1,1,1,1,1] => 63
[7,6] => 72
[7,5,1] => 71
[7,4,2] => 70
[7,4,1,1] => 69
[7,3,3] => 69
[7,3,2,1] => 68
[7,3,1,1,1] => 66
[7,2,2,2] => 66
[7,2,2,1,1] => 65
[7,2,1,1,1,1] => 62
[7,1,1,1,1,1,1] => 57
[6,6,1] => 70
[6,5,2] => 69
[6,5,1,1] => 68
[6,4,3] => 68
[6,4,2,1] => 67
[6,4,1,1,1] => 65
[6,3,3,1] => 66
[6,3,2,2] => 65
[6,3,2,1,1] => 64
[6,3,1,1,1,1] => 61
[6,2,2,2,1] => 62
[6,2,2,1,1,1] => 60
[6,2,1,1,1,1,1] => 56
[6,1,1,1,1,1,1,1] => 50
[5,5,3] => 67
[5,5,2,1] => 66
[5,5,1,1,1] => 64
[5,4,4] => 66
[5,4,3,1] => 65
[5,4,2,2] => 64
[5,4,2,1,1] => 63
[5,4,1,1,1,1] => 60
[5,3,3,2] => 63
[5,3,3,1,1] => 62
[5,3,2,2,1] => 61
[5,3,2,1,1,1] => 59
[5,3,1,1,1,1,1] => 55
[5,2,2,2,2] => 58
[5,2,2,2,1,1] => 57
[5,2,2,1,1,1,1] => 54
[5,2,1,1,1,1,1,1] => 49
[5,1,1,1,1,1,1,1,1] => 42
[4,4,4,1] => 63
[4,4,3,2] => 62
[4,4,3,1,1] => 61
[4,4,2,2,1] => 60
[4,4,2,1,1,1] => 58
[4,4,1,1,1,1,1] => 54
[4,3,3,3] => 60
[4,3,3,2,1] => 59
[4,3,3,1,1,1] => 57
[4,3,2,2,2] => 57
[4,3,2,2,1,1] => 56
[4,3,2,1,1,1,1] => 53
[4,3,1,1,1,1,1,1] => 48
[4,2,2,2,2,1] => 53
[4,2,2,2,1,1,1] => 51
[4,2,2,1,1,1,1,1] => 47
[4,2,1,1,1,1,1,1,1] => 41
[4,1,1,1,1,1,1,1,1,1] => 33
[3,3,3,3,1] => 56
[3,3,3,2,2] => 55
[3,3,3,2,1,1] => 54
[3,3,3,1,1,1,1] => 51
[3,3,2,2,2,1] => 52
[3,3,2,2,1,1,1] => 50
[3,3,2,1,1,1,1,1] => 46
[3,3,1,1,1,1,1,1,1] => 40
[3,2,2,2,2,2] => 48
[3,2,2,2,2,1,1] => 47
[3,2,2,2,1,1,1,1] => 44
[3,2,2,1,1,1,1,1,1] => 39
[3,2,1,1,1,1,1,1,1,1] => 32
[3,1,1,1,1,1,1,1,1,1,1] => 23
[2,2,2,2,2,2,1] => 42
[2,2,2,2,2,1,1,1] => 40
[2,2,2,2,1,1,1,1,1] => 36
[2,2,2,1,1,1,1,1,1,1] => 30
[2,2,1,1,1,1,1,1,1,1,1] => 22
[2,1,1,1,1,1,1,1,1,1,1,1] => 12
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[14] => 91
[13,1] => 90
[12,2] => 89
[12,1,1] => 88
[11,3] => 88
[11,2,1] => 87
[11,1,1,1] => 85
[10,4] => 87
[10,3,1] => 86
[10,2,2] => 85
[10,2,1,1] => 84
[10,1,1,1,1] => 81
[9,5] => 86
[9,4,1] => 85
[9,3,2] => 84
[9,3,1,1] => 83
[9,2,2,1] => 82
[9,2,1,1,1] => 80
[9,1,1,1,1,1] => 76
[8,6] => 85
[8,5,1] => 84
[8,4,2] => 83
[8,4,1,1] => 82
[8,3,3] => 82
[8,3,2,1] => 81
[8,3,1,1,1] => 79
[8,2,2,2] => 79
[8,2,2,1,1] => 78
[8,2,1,1,1,1] => 75
[8,1,1,1,1,1,1] => 70
[7,7] => 84
[7,6,1] => 83
[7,5,2] => 82
[7,5,1,1] => 81
[7,4,3] => 81
[7,4,2,1] => 80
[7,4,1,1,1] => 78
[7,3,3,1] => 79
[7,3,2,2] => 78
[7,3,2,1,1] => 77
[7,3,1,1,1,1] => 74
[7,2,2,2,1] => 75
[7,2,2,1,1,1] => 73
[7,2,1,1,1,1,1] => 69
[7,1,1,1,1,1,1,1] => 63
[6,6,2] => 81
[6,6,1,1] => 80
[6,5,3] => 80
[6,5,2,1] => 79
[6,5,1,1,1] => 77
[6,4,4] => 79
[6,4,3,1] => 78
[6,4,2,2] => 77
[6,4,2,1,1] => 76
[6,4,1,1,1,1] => 73
[6,3,3,2] => 76
[6,3,3,1,1] => 75
[6,3,2,2,1] => 74
[6,3,2,1,1,1] => 72
[6,3,1,1,1,1,1] => 68
[6,2,2,2,2] => 71
[6,2,2,2,1,1] => 70
[6,2,2,1,1,1,1] => 67
[6,2,1,1,1,1,1,1] => 62
[6,1,1,1,1,1,1,1,1] => 55
[5,5,4] => 78
[5,5,3,1] => 77
[5,5,2,2] => 76
[5,5,2,1,1] => 75
[5,5,1,1,1,1] => 72
[5,4,4,1] => 76
[5,4,3,2] => 75
[5,4,3,1,1] => 74
[5,4,2,2,1] => 73
[5,4,2,1,1,1] => 71
[5,4,1,1,1,1,1] => 67
[5,3,3,3] => 73
[5,3,3,2,1] => 72
[5,3,3,1,1,1] => 70
[5,3,2,2,2] => 70
[5,3,2,2,1,1] => 69
[5,3,2,1,1,1,1] => 66
[5,3,1,1,1,1,1,1] => 61
[5,2,2,2,2,1] => 66
[5,2,2,2,1,1,1] => 64
[5,2,2,1,1,1,1,1] => 60
[5,2,1,1,1,1,1,1,1] => 54
[5,1,1,1,1,1,1,1,1,1] => 46
[4,4,4,2] => 73
[4,4,4,1,1] => 72
[4,4,3,3] => 72
[4,4,3,2,1] => 71
[4,4,3,1,1,1] => 69
[4,4,2,2,2] => 69
[4,4,2,2,1,1] => 68
[4,4,2,1,1,1,1] => 65
[4,4,1,1,1,1,1,1] => 60
[4,3,3,3,1] => 69
[4,3,3,2,2] => 68
[4,3,3,2,1,1] => 67
[4,3,3,1,1,1,1] => 64
[4,3,2,2,2,1] => 65
[4,3,2,2,1,1,1] => 63
[4,3,2,1,1,1,1,1] => 59
[4,3,1,1,1,1,1,1,1] => 53
[4,2,2,2,2,2] => 61
[4,2,2,2,2,1,1] => 60
[4,2,2,2,1,1,1,1] => 57
[4,2,2,1,1,1,1,1,1] => 52
[4,2,1,1,1,1,1,1,1,1] => 45
[4,1,1,1,1,1,1,1,1,1,1] => 36
[3,3,3,3,2] => 65
[3,3,3,3,1,1] => 64
[3,3,3,2,2,1] => 63
[3,3,3,2,1,1,1] => 61
[3,3,3,1,1,1,1,1] => 57
[3,3,2,2,2,2] => 60
[3,3,2,2,2,1,1] => 59
[3,3,2,2,1,1,1,1] => 56
[3,3,2,1,1,1,1,1,1] => 51
[3,3,1,1,1,1,1,1,1,1] => 44
[3,2,2,2,2,2,1] => 55
[3,2,2,2,2,1,1,1] => 53
[3,2,2,2,1,1,1,1,1] => 49
[3,2,2,1,1,1,1,1,1,1] => 43
[3,2,1,1,1,1,1,1,1,1,1] => 35
[3,1,1,1,1,1,1,1,1,1,1,1] => 25
[2,2,2,2,2,2,2] => 49
[2,2,2,2,2,2,1,1] => 48
[2,2,2,2,2,1,1,1,1] => 45
[2,2,2,2,1,1,1,1,1,1] => 40
[2,2,2,1,1,1,1,1,1,1,1] => 33
[2,2,1,1,1,1,1,1,1,1,1,1] => 24
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 13
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[15] => 105
[14,1] => 104
[13,2] => 103
[13,1,1] => 102
[12,3] => 102
[12,2,1] => 101
[12,1,1,1] => 99
[11,4] => 101
[11,3,1] => 100
[11,2,2] => 99
[11,2,1,1] => 98
[11,1,1,1,1] => 95
[10,5] => 100
[10,4,1] => 99
[10,3,2] => 98
[10,3,1,1] => 97
[10,2,2,1] => 96
[10,2,1,1,1] => 94
[10,1,1,1,1,1] => 90
[9,6] => 99
[9,5,1] => 98
[9,4,2] => 97
[9,4,1,1] => 96
[9,3,3] => 96
[9,3,2,1] => 95
[9,3,1,1,1] => 93
[9,2,2,2] => 93
[9,2,2,1,1] => 92
[9,2,1,1,1,1] => 89
[9,1,1,1,1,1,1] => 84
[8,7] => 98
[8,6,1] => 97
[8,5,2] => 96
[8,5,1,1] => 95
[8,4,3] => 95
[8,4,2,1] => 94
[8,4,1,1,1] => 92
[8,3,3,1] => 93
[8,3,2,2] => 92
[8,3,2,1,1] => 91
[8,3,1,1,1,1] => 88
[8,2,2,2,1] => 89
[8,2,2,1,1,1] => 87
[8,2,1,1,1,1,1] => 83
[8,1,1,1,1,1,1,1] => 77
[7,7,1] => 96
[7,6,2] => 95
[7,6,1,1] => 94
[7,5,3] => 94
[7,5,2,1] => 93
[7,5,1,1,1] => 91
[7,4,4] => 93
[7,4,3,1] => 92
[7,4,2,2] => 91
[7,4,2,1,1] => 90
[7,4,1,1,1,1] => 87
[7,3,3,2] => 90
[7,3,3,1,1] => 89
[7,3,2,2,1] => 88
[7,3,2,1,1,1] => 86
[7,3,1,1,1,1,1] => 82
[7,2,2,2,2] => 85
[7,2,2,2,1,1] => 84
[7,2,2,1,1,1,1] => 81
[7,2,1,1,1,1,1,1] => 76
[7,1,1,1,1,1,1,1,1] => 69
[6,6,3] => 93
[6,6,2,1] => 92
[6,6,1,1,1] => 90
[6,5,4] => 92
[6,5,3,1] => 91
[6,5,2,2] => 90
[6,5,2,1,1] => 89
[6,5,1,1,1,1] => 86
[6,4,4,1] => 90
[6,4,3,2] => 89
[6,4,3,1,1] => 88
[6,4,2,2,1] => 87
[6,4,2,1,1,1] => 85
[6,4,1,1,1,1,1] => 81
[6,3,3,3] => 87
[6,3,3,2,1] => 86
[6,3,3,1,1,1] => 84
[6,3,2,2,2] => 84
[6,3,2,2,1,1] => 83
[6,3,2,1,1,1,1] => 80
[6,3,1,1,1,1,1,1] => 75
[6,2,2,2,2,1] => 80
[6,2,2,2,1,1,1] => 78
[6,2,2,1,1,1,1,1] => 74
[6,2,1,1,1,1,1,1,1] => 68
[6,1,1,1,1,1,1,1,1,1] => 60
[5,5,5] => 90
[5,5,4,1] => 89
[5,5,3,2] => 88
[5,5,3,1,1] => 87
[5,5,2,2,1] => 86
[5,5,2,1,1,1] => 84
[5,5,1,1,1,1,1] => 80
[5,4,4,2] => 87
[5,4,4,1,1] => 86
[5,4,3,3] => 86
[5,4,3,2,1] => 85
[5,4,3,1,1,1] => 83
[5,4,2,2,2] => 83
[5,4,2,2,1,1] => 82
[5,4,2,1,1,1,1] => 79
[5,4,1,1,1,1,1,1] => 74
[5,3,3,3,1] => 83
[5,3,3,2,2] => 82
[5,3,3,2,1,1] => 81
[5,3,3,1,1,1,1] => 78
[5,3,2,2,2,1] => 79
[5,3,2,2,1,1,1] => 77
[5,3,2,1,1,1,1,1] => 73
[5,3,1,1,1,1,1,1,1] => 67
[5,2,2,2,2,2] => 75
[5,2,2,2,2,1,1] => 74
[5,2,2,2,1,1,1,1] => 71
[5,2,2,1,1,1,1,1,1] => 66
[5,2,1,1,1,1,1,1,1,1] => 59
[5,1,1,1,1,1,1,1,1,1,1] => 50
[4,4,4,3] => 84
[4,4,4,2,1] => 83
[4,4,4,1,1,1] => 81
[4,4,3,3,1] => 82
[4,4,3,2,2] => 81
[4,4,3,2,1,1] => 80
[4,4,3,1,1,1,1] => 77
[4,4,2,2,2,1] => 78
[4,4,2,2,1,1,1] => 76
[4,4,2,1,1,1,1,1] => 72
[4,4,1,1,1,1,1,1,1] => 66
[4,3,3,3,2] => 79
[4,3,3,3,1,1] => 78
[4,3,3,2,2,1] => 77
[4,3,3,2,1,1,1] => 75
[4,3,3,1,1,1,1,1] => 71
[4,3,2,2,2,2] => 74
[4,3,2,2,2,1,1] => 73
[4,3,2,2,1,1,1,1] => 70
[4,3,2,1,1,1,1,1,1] => 65
[4,3,1,1,1,1,1,1,1,1] => 58
[4,2,2,2,2,2,1] => 69
[4,2,2,2,2,1,1,1] => 67
[4,2,2,2,1,1,1,1,1] => 63
[4,2,2,1,1,1,1,1,1,1] => 57
[4,2,1,1,1,1,1,1,1,1,1] => 49
[4,1,1,1,1,1,1,1,1,1,1,1] => 39
[3,3,3,3,3] => 75
[3,3,3,3,2,1] => 74
[3,3,3,3,1,1,1] => 72
[3,3,3,2,2,2] => 72
[3,3,3,2,2,1,1] => 71
[3,3,3,2,1,1,1,1] => 68
[3,3,3,1,1,1,1,1,1] => 63
[3,3,2,2,2,2,1] => 68
[3,3,2,2,2,1,1,1] => 66
[3,3,2,2,1,1,1,1,1] => 62
[3,3,2,1,1,1,1,1,1,1] => 56
[3,3,1,1,1,1,1,1,1,1,1] => 48
[3,2,2,2,2,2,2] => 63
[3,2,2,2,2,2,1,1] => 62
[3,2,2,2,2,1,1,1,1] => 59
[3,2,2,2,1,1,1,1,1,1] => 54
[3,2,2,1,1,1,1,1,1,1,1] => 47
[3,2,1,1,1,1,1,1,1,1,1,1] => 38
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 27
[2,2,2,2,2,2,2,1] => 56
[2,2,2,2,2,2,1,1,1] => 54
[2,2,2,2,2,1,1,1,1,1] => 50
[2,2,2,2,1,1,1,1,1,1,1] => 44
[2,2,2,1,1,1,1,1,1,1,1,1] => 36
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 26
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 14
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[16] => 120
[15,1] => 119
[14,2] => 118
[14,1,1] => 117
[13,3] => 117
[13,2,1] => 116
[13,1,1,1] => 114
[12,4] => 116
[12,3,1] => 115
[12,2,2] => 114
[12,2,1,1] => 113
[12,1,1,1,1] => 110
[11,5] => 115
[11,4,1] => 114
[11,3,2] => 113
[11,3,1,1] => 112
[11,2,2,1] => 111
[11,2,1,1,1] => 109
[11,1,1,1,1,1] => 105
[10,6] => 114
[10,5,1] => 113
[10,4,2] => 112
[10,4,1,1] => 111
[10,3,3] => 111
[10,3,2,1] => 110
[10,3,1,1,1] => 108
[10,2,2,2] => 108
[10,2,2,1,1] => 107
[10,2,1,1,1,1] => 104
[10,1,1,1,1,1,1] => 99
[9,7] => 113
[9,6,1] => 112
[9,5,2] => 111
[9,5,1,1] => 110
[9,4,3] => 110
[9,4,2,1] => 109
[9,4,1,1,1] => 107
[9,3,3,1] => 108
[9,3,2,2] => 107
[9,3,2,1,1] => 106
[9,3,1,1,1,1] => 103
[9,2,2,2,1] => 104
[9,2,2,1,1,1] => 102
[9,2,1,1,1,1,1] => 98
[9,1,1,1,1,1,1,1] => 92
[8,8] => 112
[8,7,1] => 111
[8,6,2] => 110
[8,6,1,1] => 109
[8,5,3] => 109
[8,5,2,1] => 108
[8,5,1,1,1] => 106
[8,4,4] => 108
[8,4,3,1] => 107
[8,4,2,2] => 106
[8,4,2,1,1] => 105
[8,4,1,1,1,1] => 102
[8,3,3,2] => 105
[8,3,3,1,1] => 104
[8,3,2,2,1] => 103
[8,3,2,1,1,1] => 101
[8,3,1,1,1,1,1] => 97
[8,2,2,2,2] => 100
[8,2,2,2,1,1] => 99
[8,2,2,1,1,1,1] => 96
[8,2,1,1,1,1,1,1] => 91
[8,1,1,1,1,1,1,1,1] => 84
[7,7,2] => 109
[7,7,1,1] => 108
[7,6,3] => 108
[7,6,2,1] => 107
[7,6,1,1,1] => 105
[7,5,4] => 107
[7,5,3,1] => 106
[7,5,2,2] => 105
[7,5,2,1,1] => 104
[7,5,1,1,1,1] => 101
[7,4,4,1] => 105
[7,4,3,2] => 104
[7,4,3,1,1] => 103
[7,4,2,2,1] => 102
[7,4,2,1,1,1] => 100
[7,4,1,1,1,1,1] => 96
[7,3,3,3] => 102
[7,3,3,2,1] => 101
[7,3,3,1,1,1] => 99
[7,3,2,2,2] => 99
[7,3,2,2,1,1] => 98
[7,3,2,1,1,1,1] => 95
[7,3,1,1,1,1,1,1] => 90
[7,2,2,2,2,1] => 95
[7,2,2,2,1,1,1] => 93
[7,2,2,1,1,1,1,1] => 89
[7,2,1,1,1,1,1,1,1] => 83
[7,1,1,1,1,1,1,1,1,1] => 75
[6,6,4] => 106
[6,6,3,1] => 105
[6,6,2,2] => 104
[6,6,2,1,1] => 103
[6,6,1,1,1,1] => 100
[6,5,5] => 105
[6,5,4,1] => 104
[6,5,3,2] => 103
[6,5,3,1,1] => 102
[6,5,2,2,1] => 101
[6,5,2,1,1,1] => 99
[6,5,1,1,1,1,1] => 95
[6,4,4,2] => 102
[6,4,4,1,1] => 101
[6,4,3,3] => 101
[6,4,3,2,1] => 100
[6,4,3,1,1,1] => 98
[6,4,2,2,2] => 98
[6,4,2,2,1,1] => 97
[6,4,2,1,1,1,1] => 94
[6,4,1,1,1,1,1,1] => 89
[6,3,3,3,1] => 98
[6,3,3,2,2] => 97
[6,3,3,2,1,1] => 96
[6,3,3,1,1,1,1] => 93
[6,3,2,2,2,1] => 94
[6,3,2,2,1,1,1] => 92
[6,3,2,1,1,1,1,1] => 88
[6,3,1,1,1,1,1,1,1] => 82
[6,2,2,2,2,2] => 90
[6,2,2,2,2,1,1] => 89
[6,2,2,2,1,1,1,1] => 86
[6,2,2,1,1,1,1,1,1] => 81
[6,2,1,1,1,1,1,1,1,1] => 74
[6,1,1,1,1,1,1,1,1,1,1] => 65
[5,5,5,1] => 102
[5,5,4,2] => 101
[5,5,4,1,1] => 100
[5,5,3,3] => 100
[5,5,3,2,1] => 99
[5,5,3,1,1,1] => 97
[5,5,2,2,2] => 97
[5,5,2,2,1,1] => 96
[5,5,2,1,1,1,1] => 93
[5,5,1,1,1,1,1,1] => 88
[5,4,4,3] => 99
[5,4,4,2,1] => 98
[5,4,4,1,1,1] => 96
[5,4,3,3,1] => 97
[5,4,3,2,2] => 96
[5,4,3,2,1,1] => 95
[5,4,3,1,1,1,1] => 92
[5,4,2,2,2,1] => 93
[5,4,2,2,1,1,1] => 91
[5,4,2,1,1,1,1,1] => 87
[5,4,1,1,1,1,1,1,1] => 81
[5,3,3,3,2] => 94
[5,3,3,3,1,1] => 93
[5,3,3,2,2,1] => 92
[5,3,3,2,1,1,1] => 90
[5,3,3,1,1,1,1,1] => 86
[5,3,2,2,2,2] => 89
[5,3,2,2,2,1,1] => 88
[5,3,2,2,1,1,1,1] => 85
[5,3,2,1,1,1,1,1,1] => 80
[5,3,1,1,1,1,1,1,1,1] => 73
[5,2,2,2,2,2,1] => 84
[5,2,2,2,2,1,1,1] => 82
[5,2,2,2,1,1,1,1,1] => 78
[5,2,2,1,1,1,1,1,1,1] => 72
[5,2,1,1,1,1,1,1,1,1,1] => 64
[5,1,1,1,1,1,1,1,1,1,1,1] => 54
[4,4,4,4] => 96
[4,4,4,3,1] => 95
[4,4,4,2,2] => 94
[4,4,4,2,1,1] => 93
[4,4,4,1,1,1,1] => 90
[4,4,3,3,2] => 93
[4,4,3,3,1,1] => 92
[4,4,3,2,2,1] => 91
[4,4,3,2,1,1,1] => 89
[4,4,3,1,1,1,1,1] => 85
[4,4,2,2,2,2] => 88
[4,4,2,2,2,1,1] => 87
[4,4,2,2,1,1,1,1] => 84
[4,4,2,1,1,1,1,1,1] => 79
[4,4,1,1,1,1,1,1,1,1] => 72
[4,3,3,3,3] => 90
[4,3,3,3,2,1] => 89
[4,3,3,3,1,1,1] => 87
[4,3,3,2,2,2] => 87
[4,3,3,2,2,1,1] => 86
[4,3,3,2,1,1,1,1] => 83
[4,3,3,1,1,1,1,1,1] => 78
[4,3,2,2,2,2,1] => 83
[4,3,2,2,2,1,1,1] => 81
[4,3,2,2,1,1,1,1,1] => 77
[4,3,2,1,1,1,1,1,1,1] => 71
[4,3,1,1,1,1,1,1,1,1,1] => 63
[4,2,2,2,2,2,2] => 78
[4,2,2,2,2,2,1,1] => 77
[4,2,2,2,2,1,1,1,1] => 74
[4,2,2,2,1,1,1,1,1,1] => 69
[4,2,2,1,1,1,1,1,1,1,1] => 62
[4,2,1,1,1,1,1,1,1,1,1,1] => 53
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 42
[3,3,3,3,3,1] => 85
[3,3,3,3,2,2] => 84
[3,3,3,3,2,1,1] => 83
[3,3,3,3,1,1,1,1] => 80
[3,3,3,2,2,2,1] => 81
[3,3,3,2,2,1,1,1] => 79
[3,3,3,2,1,1,1,1,1] => 75
[3,3,3,1,1,1,1,1,1,1] => 69
[3,3,2,2,2,2,2] => 77
[3,3,2,2,2,2,1,1] => 76
[3,3,2,2,2,1,1,1,1] => 73
[3,3,2,2,1,1,1,1,1,1] => 68
[3,3,2,1,1,1,1,1,1,1,1] => 61
[3,3,1,1,1,1,1,1,1,1,1,1] => 52
[3,2,2,2,2,2,2,1] => 71
[3,2,2,2,2,2,1,1,1] => 69
[3,2,2,2,2,1,1,1,1,1] => 65
[3,2,2,2,1,1,1,1,1,1,1] => 59
[3,2,2,1,1,1,1,1,1,1,1,1] => 51
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 41
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 29
[2,2,2,2,2,2,2,2] => 64
[2,2,2,2,2,2,2,1,1] => 63
[2,2,2,2,2,2,1,1,1,1] => 60
[2,2,2,2,2,1,1,1,1,1,1] => 55
[2,2,2,2,1,1,1,1,1,1,1,1] => 48
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 39
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 28
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 15
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[17] => 136
[16,1] => 135
[15,2] => 134
[15,1,1] => 133
[14,3] => 133
[14,2,1] => 132
[14,1,1,1] => 130
[13,4] => 132
[13,3,1] => 131
[13,2,2] => 130
[13,2,1,1] => 129
[13,1,1,1,1] => 126
[12,5] => 131
[12,4,1] => 130
[12,3,2] => 129
[12,3,1,1] => 128
[12,2,2,1] => 127
[12,2,1,1,1] => 125
[12,1,1,1,1,1] => 121
[11,6] => 130
[11,5,1] => 129
[11,4,2] => 128
[11,4,1,1] => 127
[11,3,3] => 127
[11,3,2,1] => 126
[11,3,1,1,1] => 124
[11,2,2,2] => 124
[11,2,2,1,1] => 123
[11,2,1,1,1,1] => 120
[11,1,1,1,1,1,1] => 115
[10,7] => 129
[10,6,1] => 128
[10,5,2] => 127
[10,5,1,1] => 126
[10,4,3] => 126
[10,4,2,1] => 125
[10,4,1,1,1] => 123
[10,3,3,1] => 124
[10,3,2,2] => 123
[10,3,2,1,1] => 122
[10,3,1,1,1,1] => 119
[10,2,2,2,1] => 120
[10,2,2,1,1,1] => 118
[10,2,1,1,1,1,1] => 114
[10,1,1,1,1,1,1,1] => 108
[9,8] => 128
[9,7,1] => 127
[9,6,2] => 126
[9,6,1,1] => 125
[9,5,3] => 125
[9,5,2,1] => 124
[9,5,1,1,1] => 122
[9,4,4] => 124
[9,4,3,1] => 123
[9,4,2,2] => 122
[9,4,2,1,1] => 121
[9,4,1,1,1,1] => 118
[9,3,3,2] => 121
[9,3,3,1,1] => 120
[9,3,2,2,1] => 119
[9,3,2,1,1,1] => 117
[9,3,1,1,1,1,1] => 113
[9,2,2,2,2] => 116
[9,2,2,2,1,1] => 115
[9,2,2,1,1,1,1] => 112
[9,2,1,1,1,1,1,1] => 107
[9,1,1,1,1,1,1,1,1] => 100
[8,8,1] => 126
[8,7,2] => 125
[8,7,1,1] => 124
[8,6,3] => 124
[8,6,2,1] => 123
[8,6,1,1,1] => 121
[8,5,4] => 123
[8,5,3,1] => 122
[8,5,2,2] => 121
[8,5,2,1,1] => 120
[8,5,1,1,1,1] => 117
[8,4,4,1] => 121
[8,4,3,2] => 120
[8,4,3,1,1] => 119
[8,4,2,2,1] => 118
[8,4,2,1,1,1] => 116
[8,4,1,1,1,1,1] => 112
[8,3,3,3] => 118
[8,3,3,2,1] => 117
[8,3,3,1,1,1] => 115
[8,3,2,2,2] => 115
[8,3,2,2,1,1] => 114
[8,3,2,1,1,1,1] => 111
[8,3,1,1,1,1,1,1] => 106
[8,2,2,2,2,1] => 111
[8,2,2,2,1,1,1] => 109
[8,2,2,1,1,1,1,1] => 105
[8,2,1,1,1,1,1,1,1] => 99
[8,1,1,1,1,1,1,1,1,1] => 91
[7,7,3] => 123
[7,7,2,1] => 122
[7,7,1,1,1] => 120
[7,6,4] => 122
[7,6,3,1] => 121
[7,6,2,2] => 120
[7,6,2,1,1] => 119
[7,6,1,1,1,1] => 116
[7,5,5] => 121
[7,5,4,1] => 120
[7,5,3,2] => 119
[7,5,3,1,1] => 118
[7,5,2,2,1] => 117
[7,5,2,1,1,1] => 115
[7,5,1,1,1,1,1] => 111
[7,4,4,2] => 118
[7,4,4,1,1] => 117
[7,4,3,3] => 117
[7,4,3,2,1] => 116
[7,4,3,1,1,1] => 114
[7,4,2,2,2] => 114
[7,4,2,2,1,1] => 113
[7,4,2,1,1,1,1] => 110
[7,4,1,1,1,1,1,1] => 105
[7,3,3,3,1] => 114
[7,3,3,2,2] => 113
[7,3,3,2,1,1] => 112
[7,3,3,1,1,1,1] => 109
[7,3,2,2,2,1] => 110
[7,3,2,2,1,1,1] => 108
[7,3,2,1,1,1,1,1] => 104
[7,3,1,1,1,1,1,1,1] => 98
[7,2,2,2,2,2] => 106
[7,2,2,2,2,1,1] => 105
[7,2,2,2,1,1,1,1] => 102
[7,2,2,1,1,1,1,1,1] => 97
[7,2,1,1,1,1,1,1,1,1] => 90
[7,1,1,1,1,1,1,1,1,1,1] => 81
[6,6,5] => 120
[6,6,4,1] => 119
[6,6,3,2] => 118
[6,6,3,1,1] => 117
[6,6,2,2,1] => 116
[6,6,2,1,1,1] => 114
[6,6,1,1,1,1,1] => 110
[6,5,5,1] => 118
[6,5,4,2] => 117
[6,5,4,1,1] => 116
[6,5,3,3] => 116
[6,5,3,2,1] => 115
[6,5,3,1,1,1] => 113
[6,5,2,2,2] => 113
[6,5,2,2,1,1] => 112
[6,5,2,1,1,1,1] => 109
[6,5,1,1,1,1,1,1] => 104
[6,4,4,3] => 115
[6,4,4,2,1] => 114
[6,4,4,1,1,1] => 112
[6,4,3,3,1] => 113
[6,4,3,2,2] => 112
[6,4,3,2,1,1] => 111
[6,4,3,1,1,1,1] => 108
[6,4,2,2,2,1] => 109
[6,4,2,2,1,1,1] => 107
[6,4,2,1,1,1,1,1] => 103
[6,4,1,1,1,1,1,1,1] => 97
[6,3,3,3,2] => 110
[6,3,3,3,1,1] => 109
[6,3,3,2,2,1] => 108
[6,3,3,2,1,1,1] => 106
[6,3,3,1,1,1,1,1] => 102
[6,3,2,2,2,2] => 105
[6,3,2,2,2,1,1] => 104
[6,3,2,2,1,1,1,1] => 101
[6,3,2,1,1,1,1,1,1] => 96
[6,3,1,1,1,1,1,1,1,1] => 89
[6,2,2,2,2,2,1] => 100
[6,2,2,2,2,1,1,1] => 98
[6,2,2,2,1,1,1,1,1] => 94
[6,2,2,1,1,1,1,1,1,1] => 88
[6,2,1,1,1,1,1,1,1,1,1] => 80
[6,1,1,1,1,1,1,1,1,1,1,1] => 70
[5,5,5,2] => 115
[5,5,5,1,1] => 114
[5,5,4,3] => 114
[5,5,4,2,1] => 113
[5,5,4,1,1,1] => 111
[5,5,3,3,1] => 112
[5,5,3,2,2] => 111
[5,5,3,2,1,1] => 110
[5,5,3,1,1,1,1] => 107
[5,5,2,2,2,1] => 108
[5,5,2,2,1,1,1] => 106
[5,5,2,1,1,1,1,1] => 102
[5,5,1,1,1,1,1,1,1] => 96
[5,4,4,4] => 112
[5,4,4,3,1] => 111
[5,4,4,2,2] => 110
[5,4,4,2,1,1] => 109
[5,4,4,1,1,1,1] => 106
[5,4,3,3,2] => 109
[5,4,3,3,1,1] => 108
[5,4,3,2,2,1] => 107
[5,4,3,2,1,1,1] => 105
[5,4,3,1,1,1,1,1] => 101
[5,4,2,2,2,2] => 104
[5,4,2,2,2,1,1] => 103
[5,4,2,2,1,1,1,1] => 100
[5,4,2,1,1,1,1,1,1] => 95
[5,4,1,1,1,1,1,1,1,1] => 88
[5,3,3,3,3] => 106
[5,3,3,3,2,1] => 105
[5,3,3,3,1,1,1] => 103
[5,3,3,2,2,2] => 103
[5,3,3,2,2,1,1] => 102
[5,3,3,2,1,1,1,1] => 99
[5,3,3,1,1,1,1,1,1] => 94
[5,3,2,2,2,2,1] => 99
[5,3,2,2,2,1,1,1] => 97
[5,3,2,2,1,1,1,1,1] => 93
[5,3,2,1,1,1,1,1,1,1] => 87
[5,3,1,1,1,1,1,1,1,1,1] => 79
[5,2,2,2,2,2,2] => 94
[5,2,2,2,2,2,1,1] => 93
[5,2,2,2,2,1,1,1,1] => 90
[5,2,2,2,1,1,1,1,1,1] => 85
[5,2,2,1,1,1,1,1,1,1,1] => 78
[5,2,1,1,1,1,1,1,1,1,1,1] => 69
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 58
[4,4,4,4,1] => 108
[4,4,4,3,2] => 107
[4,4,4,3,1,1] => 106
[4,4,4,2,2,1] => 105
[4,4,4,2,1,1,1] => 103
[4,4,4,1,1,1,1,1] => 99
[4,4,3,3,3] => 105
[4,4,3,3,2,1] => 104
[4,4,3,3,1,1,1] => 102
[4,4,3,2,2,2] => 102
[4,4,3,2,2,1,1] => 101
[4,4,3,2,1,1,1,1] => 98
[4,4,3,1,1,1,1,1,1] => 93
[4,4,2,2,2,2,1] => 98
[4,4,2,2,2,1,1,1] => 96
[4,4,2,2,1,1,1,1,1] => 92
[4,4,2,1,1,1,1,1,1,1] => 86
[4,4,1,1,1,1,1,1,1,1,1] => 78
[4,3,3,3,3,1] => 101
[4,3,3,3,2,2] => 100
[4,3,3,3,2,1,1] => 99
[4,3,3,3,1,1,1,1] => 96
[4,3,3,2,2,2,1] => 97
[4,3,3,2,2,1,1,1] => 95
[4,3,3,2,1,1,1,1,1] => 91
[4,3,3,1,1,1,1,1,1,1] => 85
[4,3,2,2,2,2,2] => 93
[4,3,2,2,2,2,1,1] => 92
[4,3,2,2,2,1,1,1,1] => 89
[4,3,2,2,1,1,1,1,1,1] => 84
[4,3,2,1,1,1,1,1,1,1,1] => 77
[4,3,1,1,1,1,1,1,1,1,1,1] => 68
[4,2,2,2,2,2,2,1] => 87
[4,2,2,2,2,2,1,1,1] => 85
[4,2,2,2,2,1,1,1,1,1] => 81
[4,2,2,2,1,1,1,1,1,1,1] => 75
[4,2,2,1,1,1,1,1,1,1,1,1] => 67
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 57
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 45
[3,3,3,3,3,2] => 96
[3,3,3,3,3,1,1] => 95
[3,3,3,3,2,2,1] => 94
[3,3,3,3,2,1,1,1] => 92
[3,3,3,3,1,1,1,1,1] => 88
[3,3,3,2,2,2,2] => 91
[3,3,3,2,2,2,1,1] => 90
[3,3,3,2,2,1,1,1,1] => 87
[3,3,3,2,1,1,1,1,1,1] => 82
[3,3,3,1,1,1,1,1,1,1,1] => 75
[3,3,2,2,2,2,2,1] => 86
[3,3,2,2,2,2,1,1,1] => 84
[3,3,2,2,2,1,1,1,1,1] => 80
[3,3,2,2,1,1,1,1,1,1,1] => 74
[3,3,2,1,1,1,1,1,1,1,1,1] => 66
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 56
[3,2,2,2,2,2,2,2] => 80
[3,2,2,2,2,2,2,1,1] => 79
[3,2,2,2,2,2,1,1,1,1] => 76
[3,2,2,2,2,1,1,1,1,1,1] => 71
[3,2,2,2,1,1,1,1,1,1,1,1] => 64
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 55
-----------------------------------------------------------------------------
Created: May 12, 2020 at 15:22 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: May 12, 2020 at 15:22 by Christian Stump