*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St001901
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.
-----------------------------------------------------------------------------
References: [1] (service unreachable) [[MathSciNet:1984625]]
-----------------------------------------------------------------------------
Code:
def statistic(la):
s = SymmetricFunctions(ZZ).s()
return max(c for _, c in s.higher_lie_character(la))
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 1
[1,1] => 1
[3] => 1
[2,1] => 1
[1,1,1] => 1
[4] => 1
[3,1] => 1
[2,2] => 1
[2,1,1] => 1
[1,1,1,1] => 1
[5] => 1
[4,1] => 2
[3,2] => 1
[3,1,1] => 1
[2,2,1] => 1
[2,1,1,1] => 1
[1,1,1,1,1] => 1
[6] => 3
[5,1] => 3
[4,2] => 2
[4,1,1] => 2
[3,3] => 1
[3,2,1] => 3
[3,1,1,1] => 1
[2,2,2] => 1
[2,2,1,1] => 1
[2,1,1,1,1] => 1
[1,1,1,1,1,1] => 1
[7] => 5
[6,1] => 6
[5,2] => 4
[5,1,1] => 4
[4,3] => 3
[4,2,1] => 5
[4,1,1,1] => 2
[3,3,1] => 2
[3,2,2] => 2
[3,2,1,1] => 3
[3,1,1,1,1] => 1
[2,2,2,1] => 1
[2,2,1,1,1] => 1
[2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1] => 1
[8] => 12
[7,1] => 13
[6,2] => 7
[6,1,1] => 8
[5,3] => 6
[5,2,1] => 9
[5,1,1,1] => 4
[4,4] => 3
[4,3,1] => 8
[4,2,2] => 3
[4,2,1,1] => 6
[4,1,1,1,1] => 2
[3,3,2] => 3
[3,3,1,1] => 3
[3,2,2,1] => 4
[3,2,1,1,1] => 3
[3,1,1,1,1,1] => 1
[2,2,2,2] => 1
[2,2,2,1,1] => 1
[2,2,1,1,1,1] => 1
[2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1] => 1
[9] => 24
[8,1] => 27
[7,2] => 16
[7,1,1] => 16
[6,3] => 13
[6,2,1] => 18
[6,1,1,1] => 8
[5,4] => 11
[5,3,1] => 15
[5,2,2] => 6
[5,2,1,1] => 11
[5,1,1,1,1] => 4
[4,4,1] => 7
[4,3,2] => 10
[4,3,1,1] => 10
[4,2,2,1] => 8
[4,2,1,1,1] => 6
[4,1,1,1,1,1] => 2
[3,3,3] => 2
[3,3,2,1] => 7
[3,3,1,1,1] => 3
[3,2,2,2] => 2
[3,2,2,1,1] => 5
[3,2,1,1,1,1] => 3
[3,1,1,1,1,1,1] => 1
[2,2,2,2,1] => 1
[2,2,2,1,1,1] => 1
[2,2,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1] => 1
[10] => 77
[9,1] => 86
[8,2] => 48
[8,1,1] => 48
[7,3] => 39
[7,2,1] => 55
[7,1,1,1] => 18
[6,4] => 32
[6,3,1] => 45
[6,2,2] => 16
[6,2,1,1] => 32
[6,1,1,1,1] => 8
[5,5] => 15
[5,4,1] => 38
[5,3,2] => 27
[5,3,1,1] => 27
[5,2,2,1] => 19
[5,2,1,1,1] => 12
[5,1,1,1,1,1] => 4
[4,4,2] => 12
[4,4,1,1] => 12
[4,3,3] => 12
[4,3,2,1] => 34
[4,3,1,1,1] => 11
[4,2,2,2] => 4
[4,2,2,1,1] => 12
[4,2,1,1,1,1] => 6
[4,1,1,1,1,1,1] => 2
[3,3,3,1] => 5
[3,3,2,2] => 6
[3,3,2,1,1] => 12
[3,3,1,1,1,1] => 3
[3,2,2,2,1] => 6
[3,2,2,1,1,1] => 5
[3,2,1,1,1,1,1] => 3
[3,1,1,1,1,1,1,1] => 1
[2,2,2,2,2] => 1
[2,2,2,2,1,1] => 1
[2,2,2,1,1,1,1] => 1
[2,2,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1] => 1
[11] => 210
[10,1] => 231
[9,2] => 138
[9,1,1] => 138
[8,3] => 99
[8,2,1] => 155
[8,1,1,1] => 56
[7,4] => 83
[7,3,1] => 113
[7,2,2] => 46
[7,2,1,1] => 83
[7,1,1,1,1] => 18
[6,5] => 77
[6,4,1] => 97
[6,3,2] => 71
[6,3,1,1] => 71
[6,2,2,1] => 54
[6,2,1,1,1] => 36
[6,1,1,1,1,1] => 8
[5,5,1] => 46
[5,4,2] => 62
[5,4,1,1] => 62
[5,3,3] => 27
[5,3,2,1] => 85
[5,3,1,1,1] => 31
[5,2,2,2] => 11
[5,2,2,1,1] => 30
[5,2,1,1,1,1] => 12
[5,1,1,1,1,1,1] => 4
[4,4,3] => 25
[4,4,2,1] => 39
[4,4,1,1,1] => 14
[4,3,3,1] => 34
[4,3,2,2] => 28
[4,3,2,1,1] => 50
[4,3,1,1,1,1] => 11
[4,2,2,2,1] => 14
[4,2,2,1,1,1] => 13
[4,2,1,1,1,1,1] => 6
[4,1,1,1,1,1,1,1] => 2
[3,3,3,2] => 8
[3,3,3,1,1] => 8
[3,3,2,2,1] => 19
[3,3,2,1,1,1] => 13
[3,3,1,1,1,1,1] => 3
[3,2,2,2,2] => 2
[3,2,2,2,1,1] => 9
[3,2,2,1,1,1,1] => 5
[3,2,1,1,1,1,1,1] => 3
[3,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,1] => 1
[2,2,2,2,1,1,1] => 1
[2,2,2,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1] => 1
[12] => 640
[11,1] => 700
[10,2] => 386
[10,1,1] => 384
[9,3] => 288
[9,2,1] => 428
[9,1,1,1] => 150
[8,4] => 246
[8,3,1] => 324
[8,2,2] => 113
[8,2,1,1] => 246
[8,1,1,1,1] => 56
[7,5] => 220
[7,4,1] => 280
[7,3,2] => 185
[7,3,1,1] => 185
[7,2,2,1] => 130
[7,2,1,1,1] => 95
[7,1,1,1,1,1] => 18
[6,6] => 109
[6,5,1] => 257
[6,4,2] => 163
[6,4,1,1] => 164
[6,3,3] => 72
[6,3,2,1] => 216
[6,3,1,1,1] => 76
[6,2,2,2] => 27
[6,2,2,1,1] => 78
[6,2,1,1,1,1] => 36
[6,1,1,1,1,1,1] => 8
[5,5,2] => 76
[5,5,1,1] => 78
[5,4,3] => 132
[5,4,2,1] => 196
[5,4,1,1,1] => 67
[5,3,3,1] => 87
[5,3,2,2] => 61
[5,3,2,1,1] => 132
[5,3,1,1,1,1] => 31
[5,2,2,2,1] => 32
[5,2,2,1,1,1] => 33
[5,2,1,1,1,1,1] => 12
[5,1,1,1,1,1,1,1] => 4
[4,4,4] => 20
[4,4,3,1] => 84
[4,4,2,2] => 31
[4,4,2,1,1] => 62
[4,4,1,1,1,1] => 14
[4,3,3,2] => 56
[4,3,3,1,1] => 55
[4,3,2,2,1] => 78
[4,3,2,1,1,1] => 57
[4,3,1,1,1,1,1] => 11
[4,2,2,2,2] => 5
[4,2,2,2,1,1] => 19
[4,2,2,1,1,1,1] => 13
[4,2,1,1,1,1,1,1] => 6
[4,1,1,1,1,1,1,1,1] => 2
[3,3,3,3] => 4
[3,3,3,2,1] => 24
[3,3,3,1,1,1] => 8
[3,3,2,2,2] => 9
[3,3,2,2,1,1] => 27
[3,3,2,1,1,1,1] => 13
[3,3,1,1,1,1,1,1] => 3
[3,2,2,2,2,1] => 7
[3,2,2,2,1,1,1] => 9
[3,2,2,1,1,1,1,1] => 5
[3,2,1,1,1,1,1,1,1] => 3
[3,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2] => 1
[2,2,2,2,2,1,1] => 1
[2,2,2,2,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1] => 1
[13] => 1650
[12,1] => 1790
[11,2] => 1000
[11,1,1] => 1000
[10,3] => 730
[10,2,1] => 1098
[10,1,1,1] => 420
[9,4] => 601
[9,3,1] => 811
[9,2,2] => 308
[9,2,1,1] => 601
[9,1,1,1,1] => 150
[8,5] => 536
[8,4,1] => 675
[8,3,2] => 466
[8,3,1,1] => 466
[8,2,2,1] => 347
[8,2,1,1,1] => 263
[8,1,1,1,1,1] => 56
[7,6] => 513
[7,5,1] => 613
[7,4,2] => 399
[7,4,1,1] => 399
[7,3,3] => 180
[7,3,2,1] => 533
[7,3,1,1,1] => 200
[7,2,2,2] => 74
[7,2,2,1,1] => 194
[7,2,1,1,1,1] => 95
[7,1,1,1,1,1,1] => 18
[6,6,1] => 297
[6,5,2] => 365
[6,5,1,1] => 368
[6,4,3] => 308
[6,4,2,1] => 465
[6,4,1,1,1] => 179
[6,3,3,1] => 210
[6,3,2,2] => 156
[6,3,2,1,1] => 308
[6,3,1,1,1,1] => 76
[6,2,2,2,1] => 87
[6,2,2,1,1,1] => 82
[6,2,1,1,1,1,1] => 36
[6,1,1,1,1,1,1,1] => 8
[5,5,3] => 146
[5,5,2,1] => 222
[5,5,1,1,1] => 84
[5,4,4] => 137
[5,4,3,1] => 368
[5,4,2,2] => 142
[5,4,2,1,1] => 273
[5,4,1,1,1,1] => 67
[5,3,3,2] => 128
[5,3,3,1,1] => 125
[5,3,2,2,1] => 187
[5,3,2,1,1,1] => 140
[5,3,1,1,1,1,1] => 31
[5,2,2,2,2] => 14
[5,2,2,2,1,1] => 46
[5,2,2,1,1,1,1] => 33
[5,2,1,1,1,1,1,1] => 12
[5,1,1,1,1,1,1,1,1] => 4
[4,4,4,1] => 59
[4,4,3,2] => 120
[4,4,3,1,1] => 120
[4,4,2,2,1] => 90
[4,4,2,1,1,1] => 67
[4,4,1,1,1,1,1] => 14
[4,3,3,3] => 37
[4,3,3,2,1] => 161
[4,3,3,1,1,1] => 59
[4,3,2,2,2] => 43
[4,3,2,2,1,1] => 116
[4,3,2,1,1,1,1] => 57
[4,3,1,1,1,1,1,1] => 11
[4,2,2,2,2,1] => 17
[4,2,2,2,1,1,1] => 19
[4,2,2,1,1,1,1,1] => 13
[4,2,1,1,1,1,1,1,1] => 6
[4,1,1,1,1,1,1,1,1,1] => 2
[3,3,3,3,1] => 12
[3,3,3,2,2] => 18
[3,3,3,2,1,1] => 37
[3,3,3,1,1,1,1] => 8
[3,3,2,2,2,1] => 29
[3,3,2,2,1,1,1] => 27
[3,3,2,1,1,1,1,1] => 13
[3,3,1,1,1,1,1,1,1] => 3
[3,2,2,2,2,2] => 3
[3,2,2,2,2,1,1] => 10
[3,2,2,2,1,1,1,1] => 9
[3,2,2,1,1,1,1,1,1] => 5
[3,2,1,1,1,1,1,1,1,1] => 3
[3,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,1] => 1
[2,2,2,2,2,1,1,1] => 1
[2,2,2,2,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[14] => 4973
[13,1] => 5346
[12,2] => 3126
[12,1,1] => 3126
[11,3] => 2140
[11,2,1] => 3402
[11,1,1,1] => 1296
[10,4] => 1753
[10,3,1] => 2354
[10,2,2] => 966
[10,2,1,1] => 1753
[10,1,1,1,1] => 420
[9,5] => 1548
[9,4,1] => 1944
[9,3,2] => 1386
[9,3,1,1] => 1386
[9,2,2,1] => 1080
[9,2,1,1,1] => 756
[9,1,1,1,1,1] => 150
[8,6] => 1452
[8,5,1] => 1743
[8,4,2] => 1179
[8,4,1,1] => 1179
[8,3,3] => 504
[8,3,2,1] => 1560
[8,3,1,1,1] => 594
[8,2,2,2] => 204
[8,2,2,1,1] => 576
[8,2,1,1,1,1] => 263
[8,1,1,1,1,1,1] => 56
[7,7] => 718
[7,6,1] => 1661
[7,5,2] => 1071
[7,5,1,1] => 1071
[7,4,3] => 844
[7,4,2,1] => 1350
[7,4,1,1,1] => 517
[7,3,3,1] => 577
[7,3,2,2] => 463
[7,3,2,1,1] => 844
[7,3,1,1,1,1] => 200
[7,2,2,2,1] => 229
[7,2,2,1,1,1] => 221
[7,2,1,1,1,1,1] => 95
[7,1,1,1,1,1,1,1] => 18
[6,6,2] => 507
[6,6,1,1] => 515
[6,5,3] => 783
[6,5,2,1] => 1244
[6,5,1,1,1] => 478
[6,4,4] => 371
[6,4,3,1] => 983
[6,4,2,2] => 412
[6,4,2,1,1] => 738
[6,4,1,1,1,1] => 179
[6,3,3,2] => 352
[6,3,3,1,1] => 346
[6,3,2,2,1] => 538
[6,3,2,1,1,1] => 380
[6,3,1,1,1,1,1] => 76
[6,2,2,2,2] => 37
[6,2,2,2,1,1] => 132
[6,2,2,1,1,1,1] => 82
[6,2,1,1,1,1,1,1] => 36
[6,1,1,1,1,1,1,1,1] => 8
[5,5,4] => 355
[5,5,3,1] => 470
[5,5,2,2] => 201
[5,5,2,1,1] => 355
[5,5,1,1,1,1] => 84
[5,4,4,1] => 440
[5,4,3,2] => 631
[5,4,3,1,1] => 631
[5,4,2,2,1] => 494
[5,4,2,1,1,1] => 344
[5,4,1,1,1,1,1] => 67
[5,3,3,3] => 92
[5,3,3,2,1] => 422
[5,3,3,1,1,1] => 156
[5,3,2,2,2] => 107
[5,3,2,2,1,1] => 309
[5,3,2,1,1,1,1] => 140
[5,3,1,1,1,1,1,1] => 31
[5,2,2,2,2,1] => 44
[5,2,2,2,1,1,1] => 50
[5,2,2,1,1,1,1,1] => 33
[5,2,1,1,1,1,1,1,1] => 12
[5,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,2] => 103
[4,4,4,1,1] => 103
[4,4,3,3] => 128
[4,4,3,2,1] => 397
[4,4,3,1,1,1] => 153
[4,4,2,2,2] => 47
[4,4,2,2,1,1] => 151
[4,4,2,1,1,1,1] => 67
[4,4,1,1,1,1,1,1] => 14
[4,3,3,3,1] => 115
[4,3,3,2,2] => 136
[4,3,3,2,1,1] => 254
[4,3,3,1,1,1,1] => 59
[4,3,2,2,2,1] => 136
[4,3,2,2,1,1,1] => 130
[4,3,2,1,1,1,1,1] => 57
[4,3,1,1,1,1,1,1,1] => 11
[4,2,2,2,2,2] => 6
[4,2,2,2,2,1,1] => 23
[4,2,2,2,1,1,1,1] => 19
[4,2,2,1,1,1,1,1,1] => 13
[4,2,1,1,1,1,1,1,1,1] => 6
[4,1,1,1,1,1,1,1,1,1,1] => 2
[3,3,3,3,2] => 20
[3,3,3,3,1,1] => 20
[3,3,3,2,2,1] => 62
[3,3,3,2,1,1,1] => 40
[3,3,3,1,1,1,1,1] => 8
[3,3,2,2,2,2] => 13
[3,3,2,2,2,1,1] => 42
[3,3,2,2,1,1,1,1] => 27
[3,3,2,1,1,1,1,1,1] => 13
[3,3,1,1,1,1,1,1,1,1] => 3
[3,2,2,2,2,2,1] => 8
[3,2,2,2,2,1,1,1] => 10
[3,2,2,2,1,1,1,1,1] => 9
[3,2,2,1,1,1,1,1,1,1] => 5
[3,2,1,1,1,1,1,1,1,1,1] => 3
[3,1,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,2] => 1
[2,2,2,2,2,2,1,1] => 1
[2,2,2,2,2,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[15] => 19522
[14,1] => 20919
[13,2] => 11264
[13,1,1] => 11264
[12,3] => 8450
[12,2,1] => 12204
[12,1,1,1] => 3786
[11,4] => 6656
[11,3,1] => 9216
[11,2,2] => 3328
[11,2,1,1] => 6656
[11,1,1,1,1] => 1350
[10,5] => 5837
[10,4,1] => 7322
[10,3,2] => 5069
[10,3,1,1] => 5069
[10,2,2,1] => 3661
[10,2,1,1,1] => 2253
[10,1,1,1,1,1] => 420
[9,6] => 5420
[9,5,1] => 6486
[9,4,2] => 4068
[9,4,1,1] => 4068
[9,3,3] => 1948
[9,3,2,1] => 5632
[9,3,1,1,1] => 1736
[9,2,2,2] => 682
[9,2,2,1,1] => 2034
[9,2,1,1,1,1] => 780
[9,1,1,1,1,1,1] => 150
[8,7] => 5232
[8,6,1] => 6096
[8,5,2] => 3648
[8,5,1,1] => 3648
[8,4,3] => 3168
[8,4,2,1] => 4576
[8,4,1,1,1] => 1428
[8,3,3,1] => 2192
[8,3,2,2] => 1584
[8,3,2,1,1] => 3168
[8,3,1,1,1,1] => 615
[8,2,2,2,1] => 768
[8,2,2,1,1,1] => 704
[8,2,1,1,1,1,1] => 263
[8,1,1,1,1,1,1,1] => 56
[7,7,1] => 2991
[7,6,2] => 3485
[7,6,1,1] => 3485
[7,5,3] => 2888
[7,5,2,1] => 4171
[7,5,1,1,1] => 1298
[7,4,4] => 1308
[7,4,3,1] => 3622
[7,4,2,2] => 1308
[7,4,2,1,1] => 2616
[7,4,1,1,1,1] => 538
[7,3,3,2] => 1253
[7,3,3,1,1] => 1253
[7,3,2,2,1] => 1811
[7,3,2,1,1,1] => 1116
[7,3,1,1,1,1,1] => 200
[7,2,2,2,2] => 112
[7,2,2,2,1,1] => 439
[7,2,2,1,1,1,1] => 225
[7,2,1,1,1,1,1,1] => 95
[7,1,1,1,1,1,1,1,1] => 18
[6,6,3] => 1405
[6,6,2,1] => 2030
[6,6,1,1,1] => 630
[6,5,4] => 2430
[6,5,3,1] => 3365
[6,5,2,2] => 1215
[6,5,2,1,1] => 2430
[6,5,1,1,1,1] => 498
[6,4,4,1] => 1524
[6,4,3,2] => 2110
[6,4,3,1,1] => 2110
[6,4,2,2,1] => 1524
[6,4,2,1,1,1] => 938
[6,4,1,1,1,1,1] => 179
[6,3,3,3] => 335
[6,3,3,2,1] => 1460
[6,3,3,1,1,1] => 450
[6,3,2,2,2] => 355
[6,3,2,2,1,1] => 1055
[6,3,2,1,1,1,1] => 390
[6,3,1,1,1,1,1,1] => 76
[6,2,2,2,2,1] => 131
[6,2,2,2,1,1,1] => 157
[6,2,2,1,1,1,1,1] => 82
[6,2,1,1,1,1,1,1,1] => 36
[6,1,1,1,1,1,1,1,1,1] => 8
[5,5,5] => 389
[5,5,4,1] => 1454
[5,5,3,2] => 1007
[5,5,3,1,1] => 1007
[5,5,2,2,1] => 727
[5,5,2,1,1,1] => 447
[5,5,1,1,1,1,1] => 84
[5,4,4,2] => 912
[5,4,4,1,1] => 912
[5,4,3,3] => 874
[5,4,3,2,1] => 2526
[5,4,3,1,1,1] => 778
[5,4,2,2,2] => 306
[5,4,2,2,1,1] => 912
[5,4,2,1,1,1,1] => 354
[5,4,1,1,1,1,1,1] => 67
[5,3,3,3,1] => 402
[5,3,3,2,2] => 437
[5,3,3,2,1,1] => 874
[5,3,3,1,1,1,1] => 160
[5,3,2,2,2,1] => 424
[5,3,2,2,1,1,1] => 389
[5,3,2,1,1,1,1,1] => 140
[5,3,1,1,1,1,1,1,1] => 31
[5,2,2,2,2,2] => 16
[5,2,2,2,2,1,1] => 78
[5,2,2,2,1,1,1,1] => 50
[5,2,2,1,1,1,1,1,1] => 33
[5,2,1,1,1,1,1,1,1,1] => 12
[5,1,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,3] => 262
[4,4,4,2,1] => 380
[4,4,4,1,1,1] => 124
[4,4,3,3,1] => 548
[4,4,3,2,2] => 396
[4,4,3,2,1,1] => 792
[4,4,3,1,1,1,1] => 158
[4,4,2,2,2,1] => 192
[4,4,2,2,1,1,1] => 176
[4,4,2,1,1,1,1,1] => 67
[4,4,1,1,1,1,1,1,1] => 14
[4,3,3,3,2] => 252
[4,3,3,3,1,1] => 252
[4,3,3,2,2,1] => 548
[4,3,3,2,1,1,1] => 338
[4,3,3,1,1,1,1,1] => 59
[4,3,2,2,2,2] => 68
[4,3,2,2,2,1,1] => 266
[4,3,2,2,1,1,1,1] => 131
[4,3,2,1,1,1,1,1,1] => 57
[4,3,1,1,1,1,1,1,1,1] => 11
[4,2,2,2,2,2,1] => 20
[4,2,2,2,2,1,1,1] => 30
[4,2,2,2,1,1,1,1,1] => 19
[4,2,2,1,1,1,1,1,1,1] => 13
[4,2,1,1,1,1,1,1,1,1,1] => 6
[4,1,1,1,1,1,1,1,1,1,1,1] => 2
[3,3,3,3,3] => 12
[3,3,3,3,2,1] => 87
[3,3,3,3,1,1,1] => 26
[3,3,3,2,2,2] => 43
[3,3,3,2,2,1,1] => 126
[3,3,3,2,1,1,1,1] => 40
[3,3,3,1,1,1,1,1,1] => 8
[3,3,2,2,2,2,1] => 47
[3,3,2,2,2,1,1,1] => 57
[3,3,2,2,1,1,1,1,1] => 27
[3,3,2,1,1,1,1,1,1,1] => 13
[3,3,1,1,1,1,1,1,1,1,1] => 3
[3,2,2,2,2,2,2] => 3
[3,2,2,2,2,2,1,1] => 14
[3,2,2,2,2,1,1,1,1] => 10
[3,2,2,2,1,1,1,1,1,1] => 9
[3,2,2,1,1,1,1,1,1,1,1] => 5
[3,2,1,1,1,1,1,1,1,1,1,1] => 3
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,2,1] => 1
[2,2,2,2,2,2,1,1,1] => 1
[2,2,2,2,2,1,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[16] => 72072
[15,1] => 76877
[14,2] => 42900
[14,1,1] => 42900
[13,3] => 30228
[13,2,1] => 46200
[13,1,1,1] => 15972
[12,4] => 24069
[12,3,1] => 32748
[12,2,2] => 12903
[12,2,1,1] => 24069
[12,1,1,1,1] => 4224
[11,5] => 20937
[11,4,1] => 26256
[11,3,2] => 18627
[11,3,1,1] => 18627
[11,2,2,1] => 14076
[11,2,1,1,1] => 9159
[11,1,1,1,1,1] => 1350
[10,6] => 19224
[10,5,1] => 23031
[10,4,2] => 15038
[10,4,1,1] => 15038
[10,3,3] => 6691
[10,3,2,1] => 20490
[10,3,1,1,1] => 7108
[10,2,2,2] => 2645
[10,2,2,1,1] => 7459
[10,2,1,1,1,1] => 2496
[10,1,1,1,1,1,1] => 420
[9,7] => 18306
[9,6,1] => 21360
[9,5,2] => 13326
[9,5,1,1] => 13326
[9,4,3] => 10936
[9,4,2,1] => 16709
[9,4,1,1,1] => 5773
[9,3,3,1] => 7434
[9,3,2,2] => 5874
[9,3,2,1,1] => 10936
[9,3,1,1,1,1] => 1942
[9,2,2,2,1] => 2939
[9,2,2,1,1,1] => 2711
[9,2,1,1,1,1,1] => 780
[9,1,1,1,1,1,1,1] => 150
[8,8] => 9010
[8,7,1] => 20595
[8,6,2] => 12515
[8,6,1,1] => 12515
[8,5,3] => 9812
[8,5,2,1] => 14992
[8,5,1,1,1] => 5180
[8,4,4] => 4521
[8,4,3,1] => 12304
[8,4,2,2] => 4846
[8,4,2,1,1] => 9042
[8,4,1,1,1,1] => 1584
[8,3,3,2] => 4366
[8,3,3,1,1] => 4366
[8,3,2,2,1] => 6608
[8,3,2,1,1,1] => 4308
[8,3,1,1,1,1,1] => 615
[8,2,2,2,2] => 419
[8,2,2,2,1,1] => 1594
[8,2,2,1,1,1,1] => 768
[8,2,1,1,1,1,1,1] => 263
[8,1,1,1,1,1,1,1,1] => 56
[7,7,2] => 6130
[7,7,1,1] => 6130
[7,6,3] => 9359
[7,6,2,1] => 14304
[7,6,1,1,1] => 4945
[7,5,4] => 8241
[7,5,3,1] => 11214
[7,5,2,2] => 4417
[7,5,2,1,1] => 8241
[7,5,1,1,1,1] => 1444
[7,4,4,1] => 5167
[7,4,3,2] => 7330
[7,4,3,1,1] => 7330
[7,4,2,2,1] => 5539
[7,4,2,1,1,1] => 3602
[7,4,1,1,1,1,1] => 538
[7,3,3,3] => 1084
[7,3,3,2,1] => 4990
[7,3,3,1,1,1] => 1737
[7,3,2,2,2] => 1291
[7,3,2,2,1,1] => 3635
[7,3,2,1,1,1,1] => 1229
[7,3,1,1,1,1,1,1] => 200
[7,2,2,2,2,1] => 479
[7,2,2,2,1,1,1] => 561
[7,2,2,1,1,1,1,1] => 225
[7,2,1,1,1,1,1,1,1] => 95
[7,1,1,1,1,1,1,1,1,1] => 18
[6,6,4] => 4013
[6,6,3,1] => 5460
[6,6,2,2] => 2151
[6,6,2,1,1] => 4013
[6,6,1,1,1,1] => 704
[6,5,5] => 3834
[6,5,4,1] => 9616
[6,5,3,2] => 6821
[6,5,3,1,1] => 6821
[6,5,2,2,1] => 5153
[6,5,2,1,1,1] => 3352
[6,5,1,1,1,1,1] => 498
[6,4,4,2] => 3138
[6,4,4,1,1] => 3138
[6,4,3,3] => 2794
[6,4,3,2,1] => 8552
[6,4,3,1,1,1] => 2964
[6,4,2,2,2] => 1104
[6,4,2,2,1,1] => 3114
[6,4,2,1,1,1,1] => 1040
[6,4,1,1,1,1,1,1] => 179
[6,3,3,3,1] => 1265
[6,3,3,2,2] => 1503
[6,3,3,2,1,1] => 2794
[6,3,3,1,1,1,1] => 501
[6,3,2,2,2,1] => 1506
[6,3,2,2,1,1,1] => 1390
[6,3,2,1,1,1,1,1] => 390
[6,3,1,1,1,1,1,1,1] => 76
[6,2,2,2,2,2] => 56
[6,2,2,2,2,1,1] => 269
[6,2,2,2,1,1,1,1] => 168
[6,2,2,1,1,1,1,1,1] => 82
[6,2,1,1,1,1,1,1,1,1] => 36
[6,1,1,1,1,1,1,1,1,1,1] => 8
[5,5,5,1] => 1531
[5,5,4,2] => 2998
[5,5,4,1,1] => 2998
[5,5,3,3] => 1335
[5,5,3,2,1] => 4086
[5,5,3,1,1,1] => 1416
[5,5,2,2,2] => 527
[5,5,2,2,1,1] => 1487
[5,5,2,1,1,1,1] => 496
[5,5,1,1,1,1,1,1] => 84
[5,4,4,3] => 2462
[5,4,4,2,1] => 3759
[5,4,4,1,1,1] => 1297
[5,4,3,3,1] => 3348
[5,4,3,2,2] => 2643
[5,4,3,2,1,1] => 4924
[5,4,3,1,1,1,1] => 871
[5,4,2,2,2,1] => 1322
[5,4,2,2,1,1,1] => 1219
[5,4,2,1,1,1,1,1] => 354
[5,4,1,1,1,1,1,1,1] => 67
[5,3,3,3,2] => 792
[5,3,3,3,1,1] => 792
[5,3,3,2,2,1] => 1801
[5,3,3,2,1,1,1] => 1176
[5,3,3,1,1,1,1,1] => 160
[5,3,2,2,2,2] => 229
[5,3,2,2,2,1,1] => 869
[5,3,2,2,1,1,1,1] => 422
[5,3,2,1,1,1,1,1,1] => 140
[5,3,1,1,1,1,1,1,1,1] => 31
[5,2,2,2,2,2,1] => 67
[5,2,2,2,2,1,1,1] => 94
[5,2,2,2,1,1,1,1,1] => 50
[5,2,2,1,1,1,1,1,1,1] => 33
[5,2,1,1,1,1,1,1,1,1,1] => 12
[5,1,1,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,4] => 188
[4,4,4,3,1] => 1028
[4,4,4,2,2] => 405
[4,4,4,2,1,1] => 755
[4,4,4,1,1,1,1] => 132
[4,4,3,3,2] => 1095
[4,4,3,3,1,1] => 1095
[4,4,3,2,2,1] => 1657
[4,4,3,2,1,1,1] => 1079
[4,4,3,1,1,1,1,1] => 158
[4,4,2,2,2,2] => 105
[4,4,2,2,2,1,1] => 400
[4,4,2,2,1,1,1,1] => 192
[4,4,2,1,1,1,1,1,1] => 67
[4,4,1,1,1,1,1,1,1,1] => 14
[4,3,3,3,3] => 162
[4,3,3,3,2,1] => 993
[4,3,3,3,1,1,1] => 346
[4,3,3,2,2,2] => 386
[4,3,3,2,2,1,1] => 1086
[4,3,3,2,1,1,1,1] => 370
[4,3,3,1,1,1,1,1,1] => 59
[4,3,2,2,2,2,1] => 287
[4,3,2,2,2,1,1,1] => 336
[4,3,2,2,1,1,1,1,1] => 131
[4,3,2,1,1,1,1,1,1,1] => 57
[4,3,1,1,1,1,1,1,1,1,1] => 11
[4,2,2,2,2,2,2] => 7
[4,2,2,2,2,2,1,1] => 40
[4,2,2,2,2,1,1,1,1] => 31
[4,2,2,2,1,1,1,1,1,1] => 19
[4,2,2,1,1,1,1,1,1,1,1] => 13
[4,2,1,1,1,1,1,1,1,1,1,1] => 6
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[3,3,3,3,3,1] => 44
[3,3,3,3,2,2] => 87
[3,3,3,3,2,1,1] => 162
[3,3,3,3,1,1,1,1] => 29
[3,3,3,2,2,2,1] => 175
[3,3,3,2,2,1,1,1] => 162
[3,3,3,2,1,1,1,1,1] => 40
[3,3,3,1,1,1,1,1,1,1] => 8
[3,3,2,2,2,2,2] => 20
[3,3,2,2,2,2,1,1] => 94
[3,3,2,2,2,1,1,1,1] => 60
[3,3,2,2,1,1,1,1,1,1] => 27
[3,3,2,1,1,1,1,1,1,1,1] => 13
[3,3,1,1,1,1,1,1,1,1,1,1] => 3
[3,2,2,2,2,2,2,1] => 10
[3,2,2,2,2,2,1,1,1] => 15
[3,2,2,2,2,1,1,1,1,1] => 10
[3,2,2,2,1,1,1,1,1,1,1] => 9
[3,2,2,1,1,1,1,1,1,1,1,1] => 5
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 3
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,2,2,2] => 1
[2,2,2,2,2,2,2,1,1] => 1
[2,2,2,2,2,2,1,1,1,1] => 1
[2,2,2,2,2,1,1,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
-----------------------------------------------------------------------------
Created: May 25, 2023 at 14:39 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: May 25, 2023 at 14:39 by Martin Rubey