edit this statistic or download as text // json
Identifier
Values
[] => 0
[1] => 1
[2] => 3
[1,1] => 3
[3] => 6
[2,1] => 5
[1,1,1] => 6
[4] => 10
[3,1] => 8
[2,2] => 8
[2,1,1] => 8
[1,1,1,1] => 10
[5] => 15
[4,1] => 12
[3,2] => 11
[3,1,1] => 11
[2,2,1] => 11
[2,1,1,1] => 12
[1,1,1,1,1] => 15
[6] => 21
[5,1] => 17
[4,2] => 15
[4,1,1] => 15
[3,3] => 15
[3,2,1] => 14
[3,1,1,1] => 15
[2,2,2] => 15
[2,2,1,1] => 15
[2,1,1,1,1] => 17
[1,1,1,1,1,1] => 21
[7] => 28
[6,1] => 23
[5,2] => 20
[5,1,1] => 20
[4,3] => 19
[4,2,1] => 18
[4,1,1,1] => 19
[3,3,1] => 18
[3,2,2] => 18
[3,2,1,1] => 18
[3,1,1,1,1] => 20
[2,2,2,1] => 19
[2,2,1,1,1] => 20
[2,1,1,1,1,1] => 23
[1,1,1,1,1,1,1] => 28
[8] => 36
[7,1] => 30
[6,2] => 26
[6,1,1] => 26
[5,3] => 24
[5,2,1] => 23
[5,1,1,1] => 24
[4,4] => 24
[4,3,1] => 22
[4,2,2] => 22
[4,2,1,1] => 22
[4,1,1,1,1] => 24
[3,3,2] => 22
[3,3,1,1] => 22
[3,2,2,1] => 22
[3,2,1,1,1] => 23
[3,1,1,1,1,1] => 26
[2,2,2,2] => 24
[2,2,2,1,1] => 24
[2,2,1,1,1,1] => 26
[2,1,1,1,1,1,1] => 30
[1,1,1,1,1,1,1,1] => 36
[9] => 45
[8,1] => 38
[7,2] => 33
[7,1,1] => 33
[6,3] => 30
[6,2,1] => 29
[6,1,1,1] => 30
[5,4] => 29
[5,3,1] => 27
[5,2,2] => 27
[5,2,1,1] => 27
[5,1,1,1,1] => 29
[4,4,1] => 27
[4,3,2] => 26
[4,3,1,1] => 26
[4,2,2,1] => 26
[4,2,1,1,1] => 27
[4,1,1,1,1,1] => 30
[3,3,3] => 27
[3,3,2,1] => 26
[3,3,1,1,1] => 27
[3,2,2,2] => 27
[3,2,2,1,1] => 27
[3,2,1,1,1,1] => 29
[3,1,1,1,1,1,1] => 33
[2,2,2,2,1] => 29
[2,2,2,1,1,1] => 30
[2,2,1,1,1,1,1] => 33
[2,1,1,1,1,1,1,1] => 38
[1,1,1,1,1,1,1,1,1] => 45
[10] => 55
[9,1] => 47
[8,2] => 41
[8,1,1] => 41
>>> Load all 757 entries. <<<
[7,3] => 37
[7,2,1] => 36
[7,1,1,1] => 37
[6,4] => 35
[6,3,1] => 33
[6,2,2] => 33
[6,2,1,1] => 33
[6,1,1,1,1] => 35
[5,5] => 35
[5,4,1] => 32
[5,3,2] => 31
[5,3,1,1] => 31
[5,2,2,1] => 31
[5,2,1,1,1] => 32
[5,1,1,1,1,1] => 35
[4,4,2] => 31
[4,4,1,1] => 31
[4,3,3] => 31
[4,3,2,1] => 30
[4,3,1,1,1] => 31
[4,2,2,2] => 31
[4,2,2,1,1] => 31
[4,2,1,1,1,1] => 33
[4,1,1,1,1,1,1] => 37
[3,3,3,1] => 31
[3,3,2,2] => 31
[3,3,2,1,1] => 31
[3,3,1,1,1,1] => 33
[3,2,2,2,1] => 32
[3,2,2,1,1,1] => 33
[3,2,1,1,1,1,1] => 36
[3,1,1,1,1,1,1,1] => 41
[2,2,2,2,2] => 35
[2,2,2,2,1,1] => 35
[2,2,2,1,1,1,1] => 37
[2,2,1,1,1,1,1,1] => 41
[2,1,1,1,1,1,1,1,1] => 47
[1,1,1,1,1,1,1,1,1,1] => 55
[11] => 66
[10,1] => 57
[9,2] => 50
[9,1,1] => 50
[8,3] => 45
[8,2,1] => 44
[8,1,1,1] => 45
[7,4] => 42
[7,3,1] => 40
[7,2,2] => 40
[7,2,1,1] => 40
[7,1,1,1,1] => 42
[6,5] => 41
[6,4,1] => 38
[6,3,2] => 37
[6,3,1,1] => 37
[6,2,2,1] => 37
[6,2,1,1,1] => 38
[6,1,1,1,1,1] => 41
[5,5,1] => 38
[5,4,2] => 36
[5,4,1,1] => 36
[5,3,3] => 36
[5,3,2,1] => 35
[5,3,1,1,1] => 36
[5,2,2,2] => 36
[5,2,2,1,1] => 36
[5,2,1,1,1,1] => 38
[5,1,1,1,1,1,1] => 42
[4,4,3] => 36
[4,4,2,1] => 35
[4,4,1,1,1] => 36
[4,3,3,1] => 35
[4,3,2,2] => 35
[4,3,2,1,1] => 35
[4,3,1,1,1,1] => 37
[4,2,2,2,1] => 36
[4,2,2,1,1,1] => 37
[4,2,1,1,1,1,1] => 40
[4,1,1,1,1,1,1,1] => 45
[3,3,3,2] => 36
[3,3,3,1,1] => 36
[3,3,2,2,1] => 36
[3,3,2,1,1,1] => 37
[3,3,1,1,1,1,1] => 40
[3,2,2,2,2] => 38
[3,2,2,2,1,1] => 38
[3,2,2,1,1,1,1] => 40
[3,2,1,1,1,1,1,1] => 44
[3,1,1,1,1,1,1,1,1] => 50
[2,2,2,2,2,1] => 41
[2,2,2,2,1,1,1] => 42
[2,2,2,1,1,1,1,1] => 45
[2,2,1,1,1,1,1,1,1] => 50
[2,1,1,1,1,1,1,1,1,1] => 57
[1,1,1,1,1,1,1,1,1,1,1] => 66
[12] => 78
[11,1] => 68
[10,2] => 60
[10,1,1] => 60
[9,3] => 54
[9,2,1] => 53
[9,1,1,1] => 54
[8,4] => 50
[8,3,1] => 48
[8,2,2] => 48
[8,2,1,1] => 48
[8,1,1,1,1] => 50
[7,5] => 48
[7,4,1] => 45
[7,3,2] => 44
[7,3,1,1] => 44
[7,2,2,1] => 44
[7,2,1,1,1] => 45
[7,1,1,1,1,1] => 48
[6,6] => 48
[6,5,1] => 44
[6,4,2] => 42
[6,4,1,1] => 42
[6,3,3] => 42
[6,3,2,1] => 41
[6,3,1,1,1] => 42
[6,2,2,2] => 42
[6,2,2,1,1] => 42
[6,2,1,1,1,1] => 44
[6,1,1,1,1,1,1] => 48
[5,5,2] => 42
[5,5,1,1] => 42
[5,4,3] => 41
[5,4,2,1] => 40
[5,4,1,1,1] => 41
[5,3,3,1] => 40
[5,3,2,2] => 40
[5,3,2,1,1] => 40
[5,3,1,1,1,1] => 42
[5,2,2,2,1] => 41
[5,2,2,1,1,1] => 42
[5,2,1,1,1,1,1] => 45
[5,1,1,1,1,1,1,1] => 50
[4,4,4] => 42
[4,4,3,1] => 40
[4,4,2,2] => 40
[4,4,2,1,1] => 40
[4,4,1,1,1,1] => 42
[4,3,3,2] => 40
[4,3,3,1,1] => 40
[4,3,2,2,1] => 40
[4,3,2,1,1,1] => 41
[4,3,1,1,1,1,1] => 44
[4,2,2,2,2] => 42
[4,2,2,2,1,1] => 42
[4,2,2,1,1,1,1] => 44
[4,2,1,1,1,1,1,1] => 48
[4,1,1,1,1,1,1,1,1] => 54
[3,3,3,3] => 42
[3,3,3,2,1] => 41
[3,3,3,1,1,1] => 42
[3,3,2,2,2] => 42
[3,3,2,2,1,1] => 42
[3,3,2,1,1,1,1] => 44
[3,3,1,1,1,1,1,1] => 48
[3,2,2,2,2,1] => 44
[3,2,2,2,1,1,1] => 45
[3,2,2,1,1,1,1,1] => 48
[3,2,1,1,1,1,1,1,1] => 53
[3,1,1,1,1,1,1,1,1,1] => 60
[2,2,2,2,2,2] => 48
[2,2,2,2,2,1,1] => 48
[2,2,2,2,1,1,1,1] => 50
[2,2,2,1,1,1,1,1,1] => 54
[2,2,1,1,1,1,1,1,1,1] => 60
[2,1,1,1,1,1,1,1,1,1,1] => 68
[1,1,1,1,1,1,1,1,1,1,1,1] => 78
[13] => 91
[12,1] => 80
[10,3] => 64
[9,4] => 59
[9,2,2] => 57
[8,5] => 56
[8,4,1] => 53
[8,3,2] => 52
[8,3,1,1] => 52
[7,6] => 55
[7,5,1] => 51
[7,4,2] => 49
[7,4,1,1] => 49
[7,3,3] => 49
[7,3,2,1] => 48
[6,6,1] => 51
[6,5,2] => 48
[6,5,1,1] => 48
[6,4,3] => 47
[6,4,2,1] => 46
[6,3,3,1] => 46
[6,3,2,2] => 46
[6,3,1,1,1,1] => 48
[6,2,2,1,1,1] => 48
[6,1,1,1,1,1,1,1] => 56
[5,5,3] => 47
[5,5,2,1] => 46
[5,4,4] => 47
[5,4,3,1] => 45
[5,4,2,2] => 45
[5,4,2,1,1] => 45
[5,4,1,1,1,1] => 47
[5,3,3,2] => 45
[5,3,3,1,1] => 45
[5,3,2,2,1] => 45
[5,3,2,1,1,1] => 46
[5,3,1,1,1,1,1] => 49
[5,2,2,2,1,1] => 47
[5,2,2,1,1,1,1] => 49
[5,2,1,1,1,1,1,1] => 53
[4,4,4,1] => 46
[4,4,3,2] => 45
[4,4,3,1,1] => 45
[4,4,2,2,1] => 45
[4,3,3,3] => 46
[4,3,3,2,1] => 45
[3,3,3,3,1] => 47
[3,3,3,2,2] => 47
[3,3,3,2,1,1] => 47
[3,3,2,2,2,1] => 48
[3,3,2,2,1,1,1] => 49
[3,3,2,1,1,1,1,1] => 52
[3,2,2,2,2,2] => 51
[3,2,2,2,2,1,1] => 51
[3,1,1,1,1,1,1,1,1,1,1] => 71
[2,2,2,2,2,2,1] => 55
[2,2,2,2,1,1,1,1,1] => 59
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 91
[14] => 105
[13,1] => 93
[12,2] => 83
[12,1,1] => 83
[11,2,1] => 74
[10,2,2] => 67
[9,5] => 65
[8,6] => 63
[8,5,1] => 59
[8,4,2] => 57
[8,3,3] => 57
[8,3,1,1,1] => 57
[7,7] => 63
[7,6,1] => 58
[7,5,2] => 55
[7,4,3] => 54
[6,6,2] => 55
[6,6,1,1] => 55
[6,5,3] => 53
[6,5,1,1,1] => 53
[6,4,4] => 53
[6,4,2,2] => 51
[6,2,2,2,2] => 53
[6,1,1,1,1,1,1,1,1] => 65
[5,5,4] => 53
[5,5,1,1,1,1] => 53
[5,4,4,1] => 51
[5,4,3,2] => 50
[5,4,3,1,1] => 50
[5,4,2,2,1] => 50
[5,4,2,1,1,1] => 51
[5,4,1,1,1,1,1] => 54
[5,3,3,3] => 51
[5,3,3,2,1] => 50
[5,3,2,2,2] => 51
[5,3,2,2,1,1] => 51
[5,3,2,1,1,1,1] => 53
[5,3,1,1,1,1,1,1] => 57
[5,2,2,2,2,1] => 53
[5,2,2,1,1,1,1,1] => 57
[4,4,4,2] => 51
[4,4,4,1,1] => 51
[4,4,3,3] => 51
[4,4,3,2,1] => 50
[4,3,2,2,2,1] => 52
[3,3,3,3,2] => 53
[3,3,3,3,1,1] => 53
[3,3,3,2,2,1] => 53
[3,3,2,2,2,2] => 55
[3,3,1,1,1,1,1,1,1,1] => 67
[3,2,2,2,2,1,1,1] => 59
[2,2,2,2,2,2,2] => 63
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 105
[15] => 120
[14,1] => 107
[12,3] => 87
[11,2,2] => 78
[9,6] => 72
[9,5,1] => 68
[9,3,2,1] => 65
[8,7] => 71
[8,5,2] => 63
[7,5,3] => 60
[6,6,3] => 60
[6,5,4] => 59
[6,5,1,1,1,1] => 59
[6,4,3,1,1] => 56
[6,3,3,3] => 57
[6,3,1,1,1,1,1,1] => 63
[6,2,2,2,2,1] => 59
[5,5,5] => 60
[5,5,2,2,1] => 56
[5,4,3,3] => 56
[5,4,3,2,1] => 55
[5,4,3,1,1,1] => 56
[5,3,2,2,2,1] => 57
[5,3,2,2,1,1,1] => 58
[5,3,1,1,1,1,1,1,1] => 66
[4,4,4,3] => 57
[4,4,4,1,1,1] => 57
[4,3,3,3,2] => 57
[3,3,3,3,3] => 60
[3,3,3,3,2,1] => 59
[3,3,3,2,2,2] => 60
[2,2,2,2,2,2,2,1] => 71
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 120
[16] => 136
[15,1] => 122
[12,4] => 92
[12,1,1,1,1] => 92
[10,6] => 82
[8,8] => 80
[8,6,2] => 70
[8,5,3] => 68
[7,6,3] => 67
[7,5,3,1] => 64
[7,3,3,2,1] => 63
[6,6,4] => 66
[6,6,2,2] => 64
[6,5,5] => 66
[6,4,3,3] => 62
[5,5,3,3] => 62
[5,5,2,2,2] => 62
[5,4,4,3] => 62
[5,4,3,2,1,1] => 61
[5,4,2,2,2,1] => 62
[4,4,4,4] => 64
[4,4,4,2,2] => 62
[4,4,3,3,2] => 62
[4,4,2,2,2,2] => 64
[4,3,3,3,3] => 64
[4,3,3,3,2,1] => 63
[3,3,3,3,2,2] => 66
[3,3,3,3,1,1,1,1] => 68
[3,3,2,2,2,2,2] => 70
[2,2,2,2,2,2,2,2] => 80
[2,2,2,2,2,2,1,1,1,1] => 82
[2,2,2,2,1,1,1,1,1,1,1,1] => 92
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 136
[17] => 153
[16,1] => 138
[9,8] => 89
[8,8,1] => 83
[8,6,3] => 75
[7,5,3,2] => 69
[6,5,3,3] => 68
[6,5,2,2,2] => 68
[6,4,4,3] => 68
[6,4,4,1,1,1] => 68
[6,3,3,3,2] => 68
[6,3,3,3,1,1] => 68
[5,5,4,3] => 68
[5,5,4,1,1,1] => 68
[5,5,2,2,2,1] => 68
[5,4,4,4] => 69
[5,4,3,2,2,1] => 67
[5,3,3,3,2,1] => 68
[4,4,4,3,2] => 68
[4,4,4,3,1,1] => 68
[4,4,4,2,2,1] => 68
[4,4,3,3,3] => 69
[3,3,3,3,3,2] => 73
[3,2,2,2,2,2,2,2] => 83
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 125
[4,4,4,3,2,1] => 74
[5,4,3,3,2,1] => 73
[6,3,3,3,2,1] => 74
[6,5,2,2,2,1] => 74
[5,5,3,3,1,1] => 73
[6,5,4,1,1,1] => 74
[5,5,3,3,2] => 73
[5,5,4,2,2] => 73
[6,4,4,2,2] => 73
[6,5,4,3] => 74
[4,4,4,3,3] => 75
[4,4,4,4,2] => 75
[5,5,4,4] => 75
[6,4,4,4] => 75
[2,2,2,2,2,2,2,2,2] => 99
[3,3,3,3,3,3] => 81
[18] => 171
[6,2,2,2,2,2,2] => 81
[6,6,6] => 81
[4,2,2,2,2,2,2,2] => 87
[10,4,4] => 87
[9,6,3] => 84
[8,6,4] => 81
[10,8] => 99
[3,3,3,3,1,1,1,1,1,1] => 87
[9,9] => 99
[7,7,1,1,1,1] => 81
[5,4,4,3,2,1] => 79
[5,5,3,3,2,1] => 79
[5,5,4,2,2,1] => 79
[6,4,4,2,2,1] => 79
[5,5,4,3,1,1] => 79
[6,4,4,3,1,1] => 79
[6,5,3,3,1,1] => 79
[5,5,4,3,2] => 79
[6,4,4,3,2] => 79
[6,5,3,3,2] => 79
[6,5,4,2,2] => 79
[6,5,4,3,1] => 79
[6,5,4,1,1,1,1] => 81
[4,4,4,4,3] => 82
[4,3,3,3,3,3] => 85
[19] => 190
[7,2,2,2,2,2,2] => 88
[7,6,6] => 88
[5,2,2,2,2,2,2,2] => 92
[13,6] => 118
[11,4,4] => 98
[9,6,4] => 90
[8,5,4,2] => 83
[8,5,5,1] => 85
[5,5,4,3,2,1] => 85
[6,4,4,3,2,1] => 85
[6,5,3,3,2,1] => 85
[6,5,4,2,2,1] => 85
[6,5,4,3,1,1] => 85
[6,5,4,3,2] => 85
[6,5,2,2,2,2,1] => 88
[6,5,4,2,1,1,1] => 86
[6,6,2,2,2,2] => 88
[7,5,4,3,1] => 86
[2,2,2,2,2,2,2,2,2,2] => 120
[3,3,3,3,3,3,2] => 96
[4,4,3,3,3,3] => 90
[4,4,4,4,4] => 90
[5,5,5,5] => 90
[20] => 210
[10,10] => 120
[8,2,2,2,2,2,2] => 96
[8,6,4,2] => 90
[8,6,6] => 96
[10,6,4] => 100
[9,8,3] => 101
[6,6,6,2] => 90
[10,7,3] => 102
[9,7,4] => 98
[9,5,5,1] => 94
[6,5,4,3,2,1] => 91
[6,3,3,3,3,2,1] => 95
[6,5,3,2,2,2,1] => 93
[6,5,4,3,1,1,1] => 92
[7,6,2,2,2,2] => 95
[6,6,5,4] => 95
[3,3,3,3,3,3,3] => 105
[4,4,4,3,3,3] => 96
[21] => 231
[11,7,3] => 113
[5,4,2,2,2,2,2,2] => 101
[11,10] => 131
[13,4,4] => 123
[7,6,6,2] => 97
[4,4,4,4,3,2,1] => 102
[6,4,3,3,3,2,1] => 100
[6,5,4,2,2,2,1] => 99
[6,5,4,3,2,1,1] => 98
[4,4,4,4,3,3] => 103
[8,6,2,2,2,2] => 103
[22] => 253
[9,6,4,3] => 105
[8,7,7] => 113
[5,4,4,4,3,2,1] => 107
[6,5,3,3,3,2,1] => 106
[6,5,4,3,2,2,1] => 105
[15,2,2,2,2] => 152
[9,6,5,3] => 112
[8,6,5,3,1] => 108
[6,4,4,4,3,2,1] => 113
[6,5,4,3,3,2,1] => 112
[3,3,3,3,3,3,3,3] => 132
[4,4,4,4,4,4] => 120
[6,6,6,6] => 120
[24] => 300
[11,7,5,1] => 130
[9,7,5,3] => 120
[8,8,8] => 132
[17,7] => 188
[12,9,3] => 144
[5,5,5,4,3,2,1] => 120
[6,5,4,4,3,2,1] => 119
[7,6,6,6] => 127
[5,4,4,4,2,2,2,2] => 125
[13,12] => 181
[15,5,5] => 165
[9,7,5,3,1] => 125
[10,7,5,3] => 130
[3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] => 165
[5,5,5,5,5] => 125
[12,10,3] => 155
[6,5,5,4,3,2,1] => 126
[6,6,4,3,3,2,2] => 127
[8,6,6,6] => 135
[9,7,5,4,1] => 132
[16,8,2] => 187
[6,6,5,4,3,2,1] => 133
[7,6,5,4,3,2] => 133
[3,3,3,3,3,3,3,3,3] => 162
[15,6,6] => 180
[7,6,5,4,3,2,1] => 140
[6,6,6,4,3,3] => 142
[4,3,3,3,3,3,3,3,3] => 166
[7,6,5,4,3,1,1,1] => 141
[10,7,6,4,1] => 150
[9,7,6,4,2] => 146
[10,8,5,4,1] => 151
[15,14] => 239
[7,6,5,4,3,2,1,1] => 148
[7,6,5,4,2,2,2,1] => 149
[10,8,6,4,1] => 159
[6,6,6,6,6] => 165
[15,15] => 255
[5,5,5,5,5,5] => 165
[6,6,6,6,3,3] => 159
[10,10,10] => 195
[9,7,5,5,3,1] => 159
[7,6,5,4,3,2,2,1] => 156
[7,6,5,3,3,3,2,1] => 157
[11,8,6,4,1] => 170
[10,8,6,4,2] => 165
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 255
[7,6,6,6,6] => 172
[7,6,5,4,3,3,2,1] => 164
[7,6,4,4,4,3,2,1] => 165
[11,8,6,5,1] => 178
[10,10,9,2] => 192
[14,9,8] => 211
[4,4,4,4,4,4,4,4] => 192
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 288
[7,6,5,4,4,3,2,1] => 172
[7,5,5,5,4,3,2,1] => 173
[16,16] => 288
[10,10,10,2] => 204
[16,8,4,2,2] => 218
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 291
[5,4,4,4,4,4,4,4] => 197
[7,6,5,5,4,3,2,1] => 180
[6,6,6,5,4,3,2,1] => 181
[22,7,4] => 306
[12,12,4,3,2] => 212
[4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 295
[7,6,6,5,4,3,2,1] => 188
[12,9,7,5,1] => 209
[7,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 280
[7,7,6,5,4,3,2,1] => 196
[13,9,7,5,1] => 222
[18,18] => 360
[24,12] => 390
[11,9,7,5,3,1] => 216
[11,8,7,5,4,1] => 214
[8,7,6,5,4,3,2,1] => 204
[8,7,7,7,7] => 218
[7,6,2,2,2,2,2,2,2,2,2,2,2,2] => 271
[7,6,6,6,6,6] => 223
[8,7,6,5,4,3,2,1,1] => 213
[8,7,6,5,4,3,2,2,1] => 222
[8,7,6,5,4,3,3,2,1] => 231
[10,10,10,10] => 280
[12,12,12,4] => 292
[8,7,6,5,4,4,3,2,1] => 240
[11,9,7,5,5,3] => 248
[4,4,4,4,4,4,4,4,4,4] => 280
[14,14,8,4] => 298
[7,6,6,6,2,2,2,2,2,2,2,2] => 271
[8,7,6,5,5,4,3,2,1] => 249
[9,9,9,9,3,3] => 273
[8,7,6,6,5,4,3,2,1] => 258
[10,10,10,5,5,2] => 273
[16,10,8,8] => 313
[26,9,7] => 447
[8,7,7,6,5,4,3,2,1] => 267
[8,8,7,6,5,4,3,2,1] => 276
[18,18,9] => 423
[9,8,7,6,5,4,3,2,1] => 285
[11,9,7,7,5,3,3] => 291
[48] => 1176
[7,6,6,6,6,6,6,6] => 343
[22,9,8,5,5] => 424
[6,6,6,6,6,6,6,3,3,2] => 351
[27,14,9] => 560
[17,14,13,8] => 449
[5,5,5,5,5,5,5,5,5,5,5] => 440
[27,20,8] => 660
[26,13,7,7,2] => 557
[31,12,10,4] => 683
[6,6,6,6,6,6,6,6,6,6] => 480
[5,5,5,5,5,5,5,5,5,5,5,5] => 510
[12,12,12,12,12] => 510
[12,12,12,12,11,4] => 524
[12,12,12,12,12,4] => 540
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 1091
[11,11,11,11,11,10] => 545
[11,11,11,11,11,11] => 561
[16,14,9,9,9,9] => 561
[8,8,8,8,8,8,8,8,4,2] => 575
[24,24,24] => 972
[16,16,16,16,8,4,2] => 753
[12,12,12,12,12,12,4,4] => 720
[22,20,20,12,8] => 915
[20,20,8,4,4,4,4,4,4,4,4,4] => 834
[33,32,9,9,5] => 1291
[18,18,18,18,18] => 1035
[18,18,18,18,9,9] => 963
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3] => 939
[56,17,11,10,5] => 1974
[33,26,23,12,9] => 1455
[22,22,22,10,10,9,4,4] => 1167
[22,22,22,10,10,10,4,4] => 1182
[12,12,12,12,12,12,12,12,4,3,2] => 1058
[24,24,24,24,14] => 1505
[76,22,9,6] => 3303
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 1610
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 1740
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 1560
[12,12,12,12,12,12,12,12,12,12] => 1320
[24,24,24,24,24] => 1740
[12,12,12,12,12,12,12,12,12,6,6,6,4,2] => 1464
[54,48,18,10,8] => 3069
[24,24,24,24,24,24] => 2160
[37,33,20,20,13,10,10,10,7] => 2389
[42,34,30,22,22,14,2] => 2907
[54,52,34,18,11,7] => 3976
[65,27,27,25,13,9,6,6] => 3735
[18,18,18,18,18,18,18,18,18,18] => 2520
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 3240
[16,16,16,16,16,16,16,8,8,8,8,8,8,8,8,4,2] => 2353
[58,38,38,38,30] => 4747
[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 3840
[10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,2] => 4428
[74,58,34,34,22,22,13,11,2] => 6939
[61,48,48,48,45,22,12,2] => 7452
[15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3] => 4805
[98,62,36,26,14,14,14,14,14,14,12,2] => 9432
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,13,2] => 6840
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,2] => 6878
[74,74,26,26,26,26,12,12,12,12,12,12,6,6,4,4,3,3,3,3] => 9034
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 11880
[64,57,40,39,28,23,19,19,16,9,8,8,8,8,8,8,6,6] => 8569
[70,70,46,28,22,22,10,9,9,9,9,8,8,8,8,8,7,7,7,3,3,3] => 9347
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,7,7,7,7,7,2] => 9491
[170,92,36,28,27,24,20,14,13,10,8,8] => 22152
[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,6,6,6,6,4,4,4,3,3] => 11607
[145,83,62,44,44,42,19,16,16,10,8] => 20709
[98,98,37,37,37,37,24,24,24,24,24,24,24,24,10,10,8,8] => 18090
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 45360
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Description
The sum of the hook lengths of an integer partition.
For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below + 1. This statistic is the sum of all hook lengths of a partition.
References
[1] Amdeberhan, T. Average on sum of hooks in a rectangle MathOverflow:273095
Code
def statistic(L):
    return sum(L.hooks())
Created
Jun 27, 2017 at 09:02 by Christian Stump
Updated
Mar 11, 2024 at 11:26 by Martin Rubey