Identifier
Values
[1] => 1
[2] => 2
[1,1] => 0
[3] => 3
[2,1] => 1
[1,1,1] => 0
[4] => 5
[3,1] => 2
[2,2] => 2
[2,1,1] => 0
[1,1,1,1] => 0
[5] => 7
[4,1] => 5
[3,2] => 4
[3,1,1] => 0
[2,2,1] => 1
[2,1,1,1] => 0
[1,1,1,1,1] => 0
[6] => 11
[5,1] => 8
[4,2] => 10
[4,1,1] => 1
[3,3] => 2
[3,2,1] => 2
[3,1,1,1] => 0
[2,2,2] => 2
[2,2,1,1] => 0
[2,1,1,1,1] => 0
[1,1,1,1,1,1] => 0
[7] => 15
[6,1] => 15
[5,2] => 17
[5,1,1] => 2
[4,3] => 10
[4,2,1] => 7
[4,1,1,1] => 0
[3,3,1] => 1
[3,2,2] => 4
[3,2,1,1] => 0
[3,1,1,1,1] => 0
[2,2,2,1] => 1
[2,2,1,1,1] => 0
[2,1,1,1,1,1] => 0
[1,1,1,1,1,1,1] => 0
[8] => 22
[7,1] => 23
[6,2] => 32
[6,1,1] => 5
[5,3] => 20
[5,2,1] => 14
[5,1,1,1] => 0
[4,4] => 12
[4,3,1] => 9
[4,2,2] => 11
[4,2,1,1] => 1
[4,1,1,1,1] => 0
[3,3,2] => 2
[3,3,1,1] => 0
[3,2,2,1] => 2
[3,2,1,1,1] => 0
[3,1,1,1,1,1] => 0
[2,2,2,2] => 2
[2,2,2,1,1] => 0
[2,2,1,1,1,1] => 0
[2,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1] => 0
[9] => 30
[8,1] => 37
[7,2] => 51
[7,1,1] => 10
[6,3] => 44
[6,2,1] => 29
[6,1,1,1] => 0
[5,4] => 27
[5,3,1] => 22
[5,2,2] => 22
[5,2,1,1] => 3
[5,1,1,1,1] => 0
[4,4,1] => 15
[4,3,2] => 14
[4,3,1,1] => 2
[4,2,2,1] => 7
[4,2,1,1,1] => 0
[4,1,1,1,1,1] => 0
[3,3,3] => 0
[3,3,2,1] => 1
[3,3,1,1,1] => 0
[3,2,2,2] => 4
[3,2,2,1,1] => 0
[3,2,1,1,1,1] => 0
[3,1,1,1,1,1,1] => 0
[2,2,2,2,1] => 1
[2,2,2,1,1,1] => 0
[2,2,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1] => 0
[10] => 42
[9,1] => 55
[8,2] => 84
[8,1,1] => 18
[7,3] => 76
>>> Load all 1200 entries. <<<[7,2,1] => 53
[7,1,1,1] => 1
[6,4] => 66
[6,3,1] => 53
[6,2,2] => 44
[6,2,1,1] => 7
[6,1,1,1,1] => 0
[5,5] => 16
[5,4,1] => 39
[5,3,2] => 36
[5,3,1,1] => 8
[5,2,2,1] => 16
[5,2,1,1,1] => 0
[5,1,1,1,1,1] => 0
[4,4,2] => 25
[4,4,1,1] => 5
[4,3,3] => 5
[4,3,2,1] => 10
[4,3,1,1,1] => 0
[4,2,2,2] => 11
[4,2,2,1,1] => 1
[4,2,1,1,1,1] => 0
[4,1,1,1,1,1,1] => 0
[3,3,3,1] => 0
[3,3,2,2] => 2
[3,3,2,1,1] => 0
[3,3,1,1,1,1] => 0
[3,2,2,2,1] => 2
[3,2,2,1,1,1] => 0
[3,2,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1] => 0
[2,2,2,2,2] => 2
[2,2,2,2,1,1] => 0
[2,2,2,1,1,1,1] => 0
[2,2,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1] => 0
[11] => 56
[10,1] => 83
[9,2] => 128
[9,1,1] => 31
[8,3] => 134
[8,2,1] => 94
[8,1,1,1] => 2
[7,4] => 121
[7,3,1] => 105
[7,2,2] => 78
[7,2,1,1] => 17
[7,1,1,1,1] => 0
[6,5] => 67
[6,4,1] => 101
[6,3,2] => 88
[6,3,1,1] => 20
[6,2,2,1] => 35
[6,2,1,1,1] => 0
[6,1,1,1,1,1] => 0
[5,5,1] => 28
[5,4,2] => 70
[5,4,1,1] => 19
[5,3,3] => 17
[5,3,2,1] => 32
[5,3,1,1,1] => 1
[5,2,2,2] => 23
[5,2,2,1,1] => 3
[5,2,1,1,1,1] => 0
[5,1,1,1,1,1,1] => 0
[4,4,3] => 22
[4,4,2,1] => 21
[4,4,1,1,1] => 0
[4,3,3,1] => 4
[4,3,2,2] => 14
[4,3,2,1,1] => 2
[4,3,1,1,1,1] => 0
[4,2,2,2,1] => 7
[4,2,2,1,1,1] => 0
[4,2,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1] => 0
[3,3,3,2] => 0
[3,3,3,1,1] => 0
[3,3,2,2,1] => 1
[3,3,2,1,1,1] => 0
[3,3,1,1,1,1,1] => 0
[3,2,2,2,2] => 4
[3,2,2,2,1,1] => 0
[3,2,2,1,1,1,1] => 0
[3,2,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,1] => 1
[2,2,2,2,1,1,1] => 0
[2,2,2,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1] => 0
[12] => 77
[11,1] => 118
[10,2] => 197
[10,1,1] => 52
[9,3] => 216
[9,2,1] => 156
[9,1,1,1] => 5
[8,4] => 223
[8,3,1] => 198
[8,2,2] => 139
[8,2,1,1] => 34
[8,1,1,1,1] => 0
[7,5] => 144
[7,4,1] => 208
[7,3,2] => 176
[7,3,1,1] => 50
[7,2,2,1] => 68
[7,2,1,1,1] => 1
[7,1,1,1,1,1] => 0
[6,6] => 68
[6,5,1] => 118
[6,4,2] => 186
[6,4,1,1] => 51
[6,3,3] => 52
[6,3,2,1] => 83
[6,3,1,1,1] => 2
[6,2,2,2] => 49
[6,2,2,1,1] => 8
[6,2,1,1,1,1] => 0
[6,1,1,1,1,1,1] => 0
[5,5,2] => 55
[5,5,1,1] => 20
[5,4,3] => 66
[5,4,2,1] => 73
[5,4,1,1,1] => 3
[5,3,3,1] => 20
[5,3,2,2] => 40
[5,3,2,1,1] => 10
[5,3,1,1,1,1] => 0
[5,2,2,2,1] => 16
[5,2,2,1,1,1] => 0
[5,2,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1] => 0
[4,4,4] => 24
[4,4,3,1] => 22
[4,4,2,2] => 27
[4,4,2,1,1] => 5
[4,4,1,1,1,1] => 0
[4,3,3,2] => 5
[4,3,3,1,1] => 1
[4,3,2,2,1] => 10
[4,3,2,1,1,1] => 0
[4,3,1,1,1,1,1] => 0
[4,2,2,2,2] => 11
[4,2,2,2,1,1] => 1
[4,2,2,1,1,1,1] => 0
[4,2,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1] => 0
[3,3,3,3] => 0
[3,3,3,2,1] => 0
[3,3,3,1,1,1] => 0
[3,3,2,2,2] => 2
[3,3,2,2,1,1] => 0
[3,3,2,1,1,1,1] => 0
[3,3,1,1,1,1,1,1] => 0
[3,2,2,2,2,1] => 2
[3,2,2,2,1,1,1] => 0
[3,2,2,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2] => 2
[2,2,2,2,2,1,1] => 0
[2,2,2,2,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[13] => 101
[12,1] => 171
[11,2] => 288
[11,1,1] => 82
[10,3] => 347
[10,2,1] => 256
[10,1,1,1] => 10
[9,4] => 372
[9,3,1] => 347
[9,2,2] => 229
[9,2,1,1] => 65
[9,1,1,1,1] => 0
[8,5] => 297
[8,4,1] => 406
[8,3,2] => 341
[8,3,1,1] => 103
[8,2,2,1] => 130
[8,2,1,1,1] => 3
[8,1,1,1,1,1] => 0
[7,6] => 176
[7,5,1] => 287
[7,4,2] => 391
[7,4,1,1] => 126
[7,3,3] => 119
[7,3,2,1] => 185
[7,3,1,1,1] => 8
[7,2,2,2] => 90
[7,2,2,1,1] => 19
[7,2,1,1,1,1] => 0
[7,1,1,1,1,1,1] => 0
[6,6,1] => 127
[6,5,2] => 234
[6,5,1,1] => 75
[6,4,3] => 194
[6,4,2,1] => 204
[6,4,1,1,1] => 8
[6,3,3,1] => 62
[6,3,2,2] => 106
[6,3,2,1,1] => 28
[6,3,1,1,1,1] => 0
[6,2,2,2,1] => 37
[6,2,2,1,1,1] => 0
[6,2,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1] => 0
[5,5,3] => 59
[5,5,2,1] => 73
[5,5,1,1,1] => 7
[5,4,4] => 68
[5,4,3,1] => 88
[5,4,2,2] => 89
[5,4,2,1,1] => 27
[5,4,1,1,1,1] => 0
[5,3,3,2] => 23
[5,3,3,1,1] => 10
[5,3,2,2,1] => 33
[5,3,2,1,1,1] => 1
[5,3,1,1,1,1,1] => 0
[5,2,2,2,2] => 23
[5,2,2,2,1,1] => 3
[5,2,2,1,1,1,1] => 0
[5,2,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1] => 0
[4,4,4,1] => 30
[4,4,3,2] => 30
[4,4,3,1,1] => 6
[4,4,2,2,1] => 21
[4,4,2,1,1,1] => 0
[4,4,1,1,1,1,1] => 0
[4,3,3,3] => 0
[4,3,3,2,1] => 4
[4,3,3,1,1,1] => 0
[4,3,2,2,2] => 14
[4,3,2,2,1,1] => 2
[4,3,2,1,1,1,1] => 0
[4,3,1,1,1,1,1,1] => 0
[4,2,2,2,2,1] => 7
[4,2,2,2,1,1,1] => 0
[4,2,2,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,1] => 0
[3,3,3,2,2] => 0
[3,3,3,2,1,1] => 0
[3,3,3,1,1,1,1] => 0
[3,3,2,2,2,1] => 1
[3,3,2,2,1,1,1] => 0
[3,3,2,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2] => 4
[3,2,2,2,2,1,1] => 0
[3,2,2,2,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,1] => 1
[2,2,2,2,2,1,1,1] => 0
[2,2,2,2,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[14] => 135
[13,1] => 238
[12,2] => 424
[12,1,1] => 127
[11,3] => 528
[11,2,1] => 401
[11,1,1,1] => 20
[10,4] => 616
[10,3,1] => 591
[10,2,2] => 376
[10,2,1,1] => 117
[10,1,1,1,1] => 0
[9,5] => 531
[9,4,1] => 729
[9,3,2] => 607
[9,3,1,1] => 203
[9,2,2,1] => 230
[9,2,1,1,1] => 8
[9,1,1,1,1,1] => 0
[8,6] => 404
[8,5,1] => 622
[8,4,2] => 787
[8,4,1,1] => 266
[8,3,3] => 250
[8,3,2,1] => 382
[8,3,1,1,1] => 20
[8,2,2,2] => 168
[8,2,2,1,1] => 41
[8,2,1,1,1,1] => 0
[8,1,1,1,1,1,1] => 0
[7,7] => 122
[7,6,1] => 383
[7,5,2] => 581
[7,5,1,1] => 215
[7,4,3] => 440
[7,4,2,1] => 474
[7,4,1,1,1] => 28
[7,3,3,1] => 161
[7,3,2,2] => 227
[7,3,2,1,1] => 73
[7,3,1,1,1,1] => 0
[7,2,2,2,1] => 74
[7,2,2,1,1,1] => 1
[7,2,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1] => 0
[6,6,2] => 262
[6,6,1,1] => 80
[6,5,3] => 286
[6,5,2,1] => 299
[6,5,1,1,1] => 20
[6,4,4] => 197
[6,4,3,1] => 270
[6,4,2,2] => 257
[6,4,2,1,1] => 82
[6,4,1,1,1,1] => 0
[6,3,3,2] => 79
[6,3,3,1,1] => 31
[6,3,2,2,1] => 93
[6,3,2,1,1,1] => 3
[6,3,1,1,1,1,1] => 0
[6,2,2,2,2] => 50
[6,2,2,2,1,1] => 8
[6,2,2,1,1,1,1] => 0
[6,2,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1] => 0
[5,5,4] => 64
[5,5,3,1] => 105
[5,5,2,2] => 86
[5,5,2,1,1] => 40
[5,5,1,1,1,1] => 1
[5,4,4,1] => 107
[5,4,3,2] => 118
[5,4,3,1,1] => 44
[5,4,2,2,1] => 80
[5,4,2,1,1,1] => 3
[5,4,1,1,1,1,1] => 0
[5,3,3,3] => 4
[5,3,3,2,1] => 24
[5,3,3,1,1,1] => 2
[5,3,2,2,2] => 40
[5,3,2,2,1,1] => 10
[5,3,2,1,1,1,1] => 0
[5,3,1,1,1,1,1,1] => 0
[5,2,2,2,2,1] => 16
[5,2,2,2,1,1,1] => 0
[5,2,2,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,2] => 47
[4,4,4,1,1] => 10
[4,4,3,3] => 10
[4,4,3,2,1] => 24
[4,4,3,1,1,1] => 0
[4,4,2,2,2] => 27
[4,4,2,2,1,1] => 5
[4,4,2,1,1,1,1] => 0
[4,4,1,1,1,1,1,1] => 0
[4,3,3,3,1] => 0
[4,3,3,2,2] => 5
[4,3,3,2,1,1] => 1
[4,3,3,1,1,1,1] => 0
[4,3,2,2,2,1] => 10
[4,3,2,2,1,1,1] => 0
[4,3,2,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2] => 11
[4,2,2,2,2,1,1] => 1
[4,2,2,2,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,2] => 0
[3,3,3,3,1,1] => 0
[3,3,3,2,2,1] => 0
[3,3,3,2,1,1,1] => 0
[3,3,3,1,1,1,1,1] => 0
[3,3,2,2,2,2] => 2
[3,3,2,2,2,1,1] => 0
[3,3,2,2,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,1] => 2
[3,2,2,2,2,1,1,1] => 0
[3,2,2,2,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2] => 2
[2,2,2,2,2,2,1,1] => 0
[2,2,2,2,2,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[15] => 176
[14,1] => 332
[13,2] => 603
[13,1,1] => 193
[12,3] => 803
[12,2,1] => 619
[12,1,1,1] => 34
[11,4] => 962
[11,3,1] => 960
[11,2,2] => 591
[11,2,1,1] => 204
[11,1,1,1,1] => 1
[10,5] => 928
[10,4,1] => 1271
[10,3,2] => 1052
[10,3,1,1] => 373
[10,2,2,1] => 399
[10,2,1,1,1] => 17
[10,1,1,1,1,1] => 0
[9,6] => 767
[9,5,1] => 1194
[9,4,2] => 1444
[9,4,1,1] => 529
[9,3,3] => 484
[9,3,2,1] => 729
[9,3,1,1,1] => 47
[9,2,2,2] => 290
[9,2,2,1,1] => 83
[9,2,1,1,1,1] => 0
[9,1,1,1,1,1,1] => 0
[8,7] => 416
[8,6,1] => 927
[8,5,2] => 1300
[8,5,1,1] => 493
[8,4,3] => 931
[8,4,2,1] => 1013
[8,4,1,1,1] => 69
[8,3,3,1] => 359
[8,3,2,2] => 471
[8,3,2,1,1] => 166
[8,3,1,1,1,1] => 1
[8,2,2,2,1] => 145
[8,2,2,1,1,1] => 3
[8,2,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1] => 0
[7,7,1] => 312
[7,6,2] => 814
[7,6,1,1] => 309
[7,5,3] => 771
[7,5,2,1] => 814
[7,5,1,1,1] => 70
[7,4,4] => 447
[7,4,3,1] => 680
[7,4,2,2] => 585
[7,4,2,1,1] => 221
[7,4,1,1,1,1] => 1
[7,3,3,2] => 208
[7,3,3,1,1] => 90
[7,3,2,2,1] => 216
[7,3,2,1,1,1] => 10
[7,3,1,1,1,1,1] => 0
[7,2,2,2,2] => 95
[7,2,2,2,1,1] => 20
[7,2,2,1,1,1,1] => 0
[7,2,1,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1,1] => 0
[6,6,3] => 366
[6,6,2,1] => 339
[6,6,1,1,1] => 18
[6,5,4] => 336
[6,5,3,1] => 471
[6,5,2,2] => 379
[6,5,2,1,1] => 154
[6,5,1,1,1,1] => 2
[6,4,4,1] => 329
[6,4,3,2] => 383
[6,4,3,1,1] => 145
[6,4,2,2,1] => 246
[6,4,2,1,1,1] => 11
[6,4,1,1,1,1,1] => 0
[6,3,3,3] => 20
[6,3,3,2,1] => 84
[6,3,3,1,1,1] => 8
[6,3,2,2,2] => 110
[6,3,2,2,1,1] => 30
[6,3,2,1,1,1,1] => 0
[6,3,1,1,1,1,1,1] => 0
[6,2,2,2,2,1] => 37
[6,2,2,2,1,1,1] => 0
[6,2,2,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1] => 0
[5,5,5] => 20
[5,5,4,1] => 136
[5,5,3,2] => 144
[5,5,3,1,1] => 79
[5,5,2,2,1] => 92
[5,5,2,1,1,1] => 10
[5,5,1,1,1,1,1] => 0
[5,4,4,2] => 170
[5,4,4,1,1] => 59
[5,4,3,3] => 52
[5,4,3,2,1] => 122
[5,4,3,1,1,1] => 8
[5,4,2,2,2] => 91
[5,4,2,2,1,1] => 27
[5,4,2,1,1,1,1] => 0
[5,4,1,1,1,1,1,1] => 0
[5,3,3,3,1] => 6
[5,3,3,2,2] => 23
[5,3,3,2,1,1] => 11
[5,3,3,1,1,1,1] => 0
[5,3,2,2,2,1] => 33
[5,3,2,2,1,1,1] => 1
[5,3,2,1,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1] => 0
[5,2,2,2,2,2] => 23
[5,2,2,2,2,1,1] => 3
[5,2,2,2,1,1,1,1] => 0
[5,2,2,1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,3] => 38
[4,4,4,2,1] => 40
[4,4,4,1,1,1] => 0
[4,4,3,3,1] => 8
[4,4,3,2,2] => 30
[4,4,3,2,1,1] => 6
[4,4,3,1,1,1,1] => 0
[4,4,2,2,2,1] => 21
[4,4,2,2,1,1,1] => 0
[4,4,2,1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1] => 0
[4,3,3,3,2] => 0
[4,3,3,3,1,1] => 0
[4,3,3,2,2,1] => 4
[4,3,3,2,1,1,1] => 0
[4,3,3,1,1,1,1,1] => 0
[4,3,2,2,2,2] => 14
[4,3,2,2,2,1,1] => 2
[4,3,2,2,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,1] => 7
[4,2,2,2,2,1,1,1] => 0
[4,2,2,2,1,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3] => 0
[3,3,3,3,2,1] => 0
[3,3,3,3,1,1,1] => 0
[3,3,3,2,2,2] => 0
[3,3,3,2,2,1,1] => 0
[3,3,3,2,1,1,1,1] => 0
[3,3,3,1,1,1,1,1,1] => 0
[3,3,2,2,2,2,1] => 1
[3,3,2,2,2,1,1,1] => 0
[3,3,2,2,1,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2] => 4
[3,2,2,2,2,2,1,1] => 0
[3,2,2,2,2,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2,1] => 1
[2,2,2,2,2,2,1,1,1] => 0
[2,2,2,2,2,1,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[16] => 231
[15,1] => 453
[14,2] => 857
[14,1,1] => 285
[13,3] => 1178
[13,2,1] => 932
[13,1,1,1] => 60
[12,4] => 1496
[12,3,1] => 1526
[12,2,2] => 919
[12,2,1,1] => 338
[12,1,1,1,1] => 2
[11,5] => 1512
[11,4,1] => 2105
[11,3,2] => 1740
[11,3,1,1] => 662
[11,2,2,1] => 663
[11,2,1,1,1] => 37
[11,1,1,1,1,1] => 0
[10,6] => 1401
[10,5,1] => 2189
[10,4,2] => 2571
[10,4,1,1] => 986
[10,3,3] => 885
[10,3,2,1] => 1332
[10,3,1,1,1] => 97
[10,2,2,2] => 497
[10,2,2,1,1] => 157
[10,2,1,1,1,1] => 0
[10,1,1,1,1,1,1] => 0
[9,7] => 915
[9,6,1] => 1893
[9,5,2] => 2557
[9,5,1,1] => 1034
[9,4,3] => 1800
[9,4,2,1] => 1988
[9,4,1,1,1] => 161
[9,3,3,1] => 743
[9,3,2,2] => 891
[9,3,2,1,1] => 350
[9,3,1,1,1,1] => 3
[9,2,2,2,1] => 267
[9,2,2,1,1,1] => 9
[9,2,1,1,1,1,1] => 0
[9,1,1,1,1,1,1,1] => 0
[8,8] => 363
[8,7,1] => 1067
[8,6,2] => 2043
[8,6,1,1] => 803
[8,5,3] => 1815
[8,5,2,1] => 1909
[8,5,1,1,1] => 176
[8,4,4] => 958
[8,4,3,1] => 1526
[8,4,2,2] => 1267
[8,4,2,1,1] => 516
[8,4,1,1,1,1] => 5
[8,3,3,2] => 483
[8,3,3,1,1] => 218
[8,3,2,2,1] => 470
[8,3,2,1,1,1] => 28
[8,3,1,1,1,1,1] => 0
[8,2,2,2,2] => 180
[8,2,2,2,1,1] => 43
[8,2,2,1,1,1,1] => 0
[8,2,1,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1,1] => 0
[7,7,2] => 692
[7,7,1,1] => 312
[7,6,3] => 1220
[7,6,2,1] => 1208
[7,6,1,1,1] => 107
[7,5,4] => 944
[7,5,3,1] => 1384
[7,5,2,2] => 1015
[7,5,2,1,1] => 469
[7,5,1,1,1,1] => 8
[7,4,4,1] => 817
[7,4,3,2] => 979
[7,4,3,1,1] => 417
[7,4,2,2,1] => 606
[7,4,2,1,1,1] => 39
[7,4,1,1,1,1,1] => 0
[7,3,3,3] => 73
[7,3,3,2,1] => 236
[7,3,3,1,1,1] => 23
[7,3,2,2,2] => 245
[7,3,2,2,1,1] => 81
[7,3,2,1,1,1,1] => 0
[7,3,1,1,1,1,1,1] => 0
[7,2,2,2,2,1] => 76
[7,2,2,2,1,1,1] => 1
[7,2,2,1,1,1,1,1] => 0
[7,2,1,1,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1,1,1] => 0
[6,6,4] => 490
[6,6,3,1] => 602
[6,6,2,2] => 452
[6,6,2,1,1] => 173
[6,6,1,1,1,1] => 1
[6,5,5] => 178
[6,5,4,1] => 665
[6,5,3,2] => 702
[6,5,3,1,1] => 324
[6,5,2,2,1] => 410
[6,5,2,1,1,1] => 35
[6,5,1,1,1,1,1] => 0
[6,4,4,2] => 542
[6,4,4,1,1] => 202
[6,4,3,3] => 190
[6,4,3,2,1] => 422
[6,4,3,1,1,1] => 34
[6,4,2,2,2] => 278
[6,4,2,2,1,1] => 90
[6,4,2,1,1,1,1] => 0
[6,4,1,1,1,1,1,1] => 0
[6,3,3,3,1] => 28
[6,3,3,2,2] => 85
[6,3,3,2,1,1] => 41
[6,3,3,1,1,1,1] => 1
[6,3,2,2,2,1] => 94
[6,3,2,2,1,1,1] => 3
[6,3,2,1,1,1,1,1] => 0
[6,3,1,1,1,1,1,1,1] => 0
[6,2,2,2,2,2] => 50
[6,2,2,2,2,1,1] => 8
[6,2,2,2,1,1,1,1] => 0
[6,2,2,1,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1,1] => 0
[5,5,5,1] => 64
[5,5,4,2] => 221
[5,5,4,1,1] => 120
[5,5,3,3] => 83
[5,5,3,2,1] => 188
[5,5,3,1,1,1] => 27
[5,5,2,2,2] => 92
[5,5,2,2,1,1] => 43
[5,5,2,1,1,1,1] => 1
[5,5,1,1,1,1,1,1] => 0
[5,4,4,3] => 148
[5,4,4,2,1] => 186
[5,4,4,1,1,1] => 11
[5,4,3,3,1] => 65
[5,4,3,2,2] => 127
[5,4,3,2,1,1] => 51
[5,4,3,1,1,1,1] => 0
[5,4,2,2,2,1] => 80
[5,4,2,2,1,1,1] => 3
[5,4,2,1,1,1,1,1] => 0
[5,4,1,1,1,1,1,1,1] => 0
[5,3,3,3,2] => 4
[5,3,3,3,1,1] => 4
[5,3,3,2,2,1] => 24
[5,3,3,2,1,1,1] => 2
[5,3,3,1,1,1,1,1] => 0
[5,3,2,2,2,2] => 40
[5,3,2,2,2,1,1] => 10
[5,3,2,2,1,1,1,1] => 0
[5,3,2,1,1,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1,1] => 0
[5,2,2,2,2,2,1] => 16
[5,2,2,2,2,1,1,1] => 0
[5,2,2,2,1,1,1,1,1] => 0
[5,2,2,1,1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,4] => 38
[4,4,4,3,1] => 37
[4,4,4,2,2] => 50
[4,4,4,2,1,1] => 10
[4,4,4,1,1,1,1] => 0
[4,4,3,3,2] => 10
[4,4,3,3,1,1] => 2
[4,4,3,2,2,1] => 24
[4,4,3,2,1,1,1] => 0
[4,4,3,1,1,1,1,1] => 0
[4,4,2,2,2,2] => 27
[4,4,2,2,2,1,1] => 5
[4,4,2,2,1,1,1,1] => 0
[4,4,2,1,1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1,1] => 0
[4,3,3,3,3] => 0
[4,3,3,3,2,1] => 0
[4,3,3,3,1,1,1] => 0
[4,3,3,2,2,2] => 5
[4,3,3,2,2,1,1] => 1
[4,3,3,2,1,1,1,1] => 0
[4,3,3,1,1,1,1,1,1] => 0
[4,3,2,2,2,2,1] => 10
[4,3,2,2,2,1,1,1] => 0
[4,3,2,2,1,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,2] => 11
[4,2,2,2,2,2,1,1] => 1
[4,2,2,2,2,1,1,1,1] => 0
[4,2,2,2,1,1,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3,1] => 0
[3,3,3,3,2,2] => 0
[3,3,3,3,2,1,1] => 0
[3,3,3,3,1,1,1,1] => 0
[3,3,3,2,2,2,1] => 0
[3,3,3,2,2,1,1,1] => 0
[3,3,3,2,1,1,1,1,1] => 0
[3,3,3,1,1,1,1,1,1,1] => 0
[3,3,2,2,2,2,2] => 2
[3,3,2,2,2,2,1,1] => 0
[3,3,2,2,2,1,1,1,1] => 0
[3,3,2,2,1,1,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2,1] => 2
[3,2,2,2,2,2,1,1,1] => 0
[3,2,2,2,2,1,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2,2] => 2
[2,2,2,2,2,2,2,1,1] => 0
[2,2,2,2,2,2,1,1,1,1] => 0
[2,2,2,2,2,1,1,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[17] => 297
[16,1] => 618
[15,2] => 1191
[15,1,1] => 415
[14,3] => 1718
[14,2,1] => 1382
[14,1,1,1] => 97
[13,4] => 2242
[13,3,1] => 2360
[13,2,2] => 1388
[13,2,1,1] => 551
[13,1,1,1,1] => 5
[12,5] => 2432
[12,4,1] => 3410
[12,3,2] => 2816
[12,3,1,1] => 1117
[12,2,2,1] => 1080
[12,2,1,1,1] => 70
[12,1,1,1,1,1] => 0
[11,6] => 2362
[11,5,1] => 3772
[11,4,2] => 4348
[11,4,1,1] => 1765
[11,3,3] => 1544
[11,3,2,1] => 2328
[11,3,1,1,1] => 196
[11,2,2,2] => 814
[11,2,2,1,1] => 286
[11,2,1,1,1,1] => 1
[11,1,1,1,1,1,1] => 0
[10,7] => 1833
[10,6,1] => 3628
[10,5,2] => 4796
[10,5,1,1] => 2007
[10,4,3] => 3329
[10,4,2,1] => 3720
[10,4,1,1,1] => 333
[10,3,3,1] => 1430
[10,3,2,2] => 1634
[10,3,2,1,1] => 688
[10,3,1,1,1,1] => 8
[10,2,2,2,1] => 479
[10,2,2,1,1,1] => 20
[10,2,1,1,1,1,1] => 0
[10,1,1,1,1,1,1,1] => 0
[9,8] => 1022
[9,7,1] => 2504
[9,6,2] => 4289
[9,6,1,1] => 1804
[9,5,3] => 3758
[9,5,2,1] => 3991
[9,5,1,1,1] => 413
[9,4,4] => 1863
[9,4,3,1] => 3148
[9,4,2,2] => 2489
[9,4,2,1,1] => 1114
[9,4,1,1,1,1] => 16
[9,3,3,2] => 1022
[9,3,3,1,1] => 483
[9,3,2,2,1] => 942
[9,3,2,1,1,1] => 70
[9,3,1,1,1,1,1] => 0
[9,2,2,2,2] => 319
[9,2,2,2,1,1] => 90
[9,2,2,1,1,1,1] => 0
[9,2,1,1,1,1,1,1] => 0
[9,1,1,1,1,1,1,1,1] => 0
[8,8,1] => 958
[8,7,2] => 2466
[8,7,1,1] => 1070
[8,6,3] => 3200
[8,6,2,1] => 3207
[8,6,1,1,1] => 315
[8,5,4] => 2308
[8,5,3,1] => 3401
[8,5,2,2] => 2431
[8,5,2,1,1] => 1172
[8,5,1,1,1,1] => 26
[8,4,4,1] => 1853
[8,4,3,2] => 2266
[8,4,3,1,1] => 1017
[8,4,2,2,1] => 1379
[8,4,2,1,1,1] => 108
[8,4,1,1,1,1,1] => 0
[8,3,3,3] => 192
[8,3,3,2,1] => 577
[8,3,3,1,1,1] => 65
[8,3,2,2,2] => 524
[8,3,2,2,1,1] => 189
[8,3,2,1,1,1,1] => 1
[8,3,1,1,1,1,1,1] => 0
[8,2,2,2,2,1] => 151
[8,2,2,2,1,1,1] => 3
[8,2,2,1,1,1,1,1] => 0
[8,2,1,1,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1,1,1] => 0
[7,7,3] => 1129
[7,7,2,1] => 1175
[7,7,1,1,1] => 143
[7,6,4] => 1697
[7,6,3,1] => 2298
[7,6,2,2] => 1555
[7,6,2,1,1] => 742
[7,6,1,1,1,1] => 13
[7,5,5] => 596
[7,5,4,1] => 2010
[7,5,3,2] => 2099
[7,5,3,1,1] => 1036
[7,5,2,2,1] => 1178
[7,5,2,1,1,1] => 121
[7,5,1,1,1,1,1] => 0
[7,4,4,2] => 1370
[7,4,4,1,1] => 576
[7,4,3,3] => 556
[7,4,3,2,1] => 1169
[7,4,3,1,1,1] => 114
[7,4,2,2,2] => 663
[7,4,2,2,1,1] => 255
[7,4,2,1,1,1,1] => 1
[7,4,1,1,1,1,1,1] => 0
[7,3,3,3,1] => 104
[7,3,3,2,2] => 236
[7,3,3,2,1,1] => 122
[7,3,3,1,1,1,1] => 2
[7,3,2,2,2,1] => 226
[7,3,2,2,1,1,1] => 11
[7,3,2,1,1,1,1,1] => 0
[7,3,1,1,1,1,1,1,1] => 0
[7,2,2,2,2,2] => 96
[7,2,2,2,2,1,1] => 20
[7,2,2,2,1,1,1,1] => 0
[7,2,2,1,1,1,1,1,1] => 0
[7,2,1,1,1,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1,1,1,1] => 0
[6,6,5] => 438
[6,6,4,1] => 963
[6,6,3,2] => 959
[6,6,3,1,1] => 403
[6,6,2,2,1] => 503
[6,6,2,1,1,1] => 38
[6,6,1,1,1,1,1] => 0
[6,5,5,1] => 427
[6,5,4,2] => 1146
[6,5,4,1,1] => 540
[6,5,3,3] => 427
[6,5,3,2,1] => 898
[6,5,3,1,1,1] => 111
[6,5,2,2,2] => 438
[6,5,2,2,1,1] => 186
[6,5,2,1,1,1,1] => 3
[6,5,1,1,1,1,1,1] => 0
[6,4,4,3] => 498
[6,4,4,2,1] => 645
[6,4,4,1,1,1] => 49
[6,4,3,3,1] => 255
[6,4,3,2,2] => 449
[6,4,3,2,1,1] => 198
[6,4,3,1,1,1,1] => 3
[6,4,2,2,2,1] => 253
[6,4,2,2,1,1,1] => 11
[6,4,2,1,1,1,1,1] => 0
[6,4,1,1,1,1,1,1,1] => 0
[6,3,3,3,2] => 24
[6,3,3,3,1,1] => 22
[6,3,3,2,2,1] => 88
[6,3,3,2,1,1,1] => 10
[6,3,3,1,1,1,1,1] => 0
[6,3,2,2,2,2] => 110
[6,3,2,2,2,1,1] => 30
[6,3,2,2,1,1,1,1] => 0
[6,3,2,1,1,1,1,1,1] => 0
[6,3,1,1,1,1,1,1,1,1] => 0
[6,2,2,2,2,2,1] => 37
[6,2,2,2,2,1,1,1] => 0
[6,2,2,2,1,1,1,1,1] => 0
[6,2,2,1,1,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1,1,1] => 0
[5,5,5,2] => 109
[5,5,5,1,1] => 88
[5,5,4,3] => 215
[5,5,4,2,1] => 322
[5,5,4,1,1,1] => 50
[5,5,3,3,1] => 137
[5,5,3,2,2] => 174
[5,5,3,2,1,1] => 109
[5,5,3,1,1,1,1] => 3
[5,5,2,2,2,1] => 93
[5,5,2,2,1,1,1] => 10
[5,5,2,1,1,1,1,1] => 0
[5,5,1,1,1,1,1,1,1] => 0
[5,4,4,4] => 131
[5,4,4,3,1] => 196
[5,4,4,2,2] => 206
[5,4,4,2,1,1] => 77
[5,4,4,1,1,1,1] => 0
[5,4,3,3,2] => 68
[5,4,3,3,1,1] => 34
[5,4,3,2,2,1] => 124
[5,4,3,2,1,1,1] => 8
[5,4,3,1,1,1,1,1] => 0
[5,4,2,2,2,2] => 91
[5,4,2,2,2,1,1] => 27
[5,4,2,2,1,1,1,1] => 0
[5,4,2,1,1,1,1,1,1] => 0
[5,4,1,1,1,1,1,1,1,1] => 0
[5,3,3,3,3] => 0
[5,3,3,3,2,1] => 6
[5,3,3,3,1,1,1] => 1
[5,3,3,2,2,2] => 23
[5,3,3,2,2,1,1] => 11
[5,3,3,2,1,1,1,1] => 0
[5,3,3,1,1,1,1,1,1] => 0
[5,3,2,2,2,2,1] => 33
[5,3,2,2,2,1,1,1] => 1
[5,3,2,2,1,1,1,1,1] => 0
[5,3,2,1,1,1,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1,1,1] => 0
[5,2,2,2,2,2,2] => 23
[5,2,2,2,2,2,1,1] => 3
[5,2,2,2,2,1,1,1,1] => 0
[5,2,2,2,1,1,1,1,1,1] => 0
[5,2,2,1,1,1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,4,1] => 46
[4,4,4,3,2] => 50
[4,4,4,3,1,1] => 10
[4,4,4,2,2,1] => 40
[4,4,4,2,1,1,1] => 0
[4,4,4,1,1,1,1,1] => 0
[4,4,3,3,3] => 0
[4,4,3,3,2,1] => 8
[4,4,3,3,1,1,1] => 0
[4,4,3,2,2,2] => 30
[4,4,3,2,2,1,1] => 6
[4,4,3,2,1,1,1,1] => 0
[4,4,3,1,1,1,1,1,1] => 0
[4,4,2,2,2,2,1] => 21
[4,4,2,2,2,1,1,1] => 0
[4,4,2,2,1,1,1,1,1] => 0
[4,4,2,1,1,1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1,1,1] => 0
[4,3,3,3,3,1] => 0
[4,3,3,3,2,2] => 0
[4,3,3,3,2,1,1] => 0
[4,3,3,3,1,1,1,1] => 0
[4,3,3,2,2,2,1] => 4
[4,3,3,2,2,1,1,1] => 0
[4,3,3,2,1,1,1,1,1] => 0
[4,3,3,1,1,1,1,1,1,1] => 0
[4,3,2,2,2,2,2] => 14
[4,3,2,2,2,2,1,1] => 2
[4,3,2,2,2,1,1,1,1] => 0
[4,3,2,2,1,1,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,2,1] => 7
[4,2,2,2,2,2,1,1,1] => 0
[4,2,2,2,2,1,1,1,1,1] => 0
[4,2,2,2,1,1,1,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3,2] => 0
[3,3,3,3,3,1,1] => 0
[3,3,3,3,2,2,1] => 0
[3,3,3,3,2,1,1,1] => 0
[3,3,3,3,1,1,1,1,1] => 0
[3,3,3,2,2,2,2] => 0
[3,3,3,2,2,2,1,1] => 0
[3,3,3,2,2,1,1,1,1] => 0
[3,3,3,2,1,1,1,1,1,1] => 0
[3,3,3,1,1,1,1,1,1,1,1] => 0
[3,3,2,2,2,2,2,1] => 1
[3,3,2,2,2,2,1,1,1] => 0
[3,3,2,2,2,1,1,1,1,1] => 0
[3,3,2,2,1,1,1,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2,2] => 4
[3,2,2,2,2,2,2,1,1] => 0
[3,2,2,2,2,2,1,1,1,1] => 0
[3,2,2,2,2,1,1,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 0
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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:
1,0,1 1,1,0,1 2,0,2,0,0,1 3,1,0,0,1,1,0,1 4,1,3,0,0,0,0,0,1,0,1,1 6,2,1,0,1,0,0,1,0,0,1,0,0,0,0,2,0,1 9,1,3,0,0,1,0,0,0,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,1
$F_{1} = q$
$F_{2} = 1 + q^{2}$
$F_{3} = 1 + q + q^{3}$
$F_{4} = 2 + 2\ q^{2} + q^{5}$
$F_{5} = 3 + q + q^{4} + q^{5} + q^{7}$
$F_{6} = 4 + q + 3\ q^{2} + q^{8} + q^{10} + q^{11}$
$F_{7} = 6 + 2\ q + q^{2} + q^{4} + q^{7} + q^{10} + 2\ q^{15} + q^{17}$
$F_{8} = 9 + q + 3\ q^{2} + q^{5} + q^{9} + q^{11} + q^{12} + q^{14} + q^{20} + q^{22} + q^{23} + q^{32}$
$F_{9} = 13 + 2\ q + q^{2} + q^{3} + q^{4} + q^{7} + q^{10} + q^{14} + q^{15} + 2\ q^{22} + q^{27} + q^{29} + q^{30} + q^{37} + q^{44} + q^{51}$
$F_{10} = 17 + 2\ q + 3\ q^{2} + 2\ q^{5} + q^{7} + q^{8} + q^{10} + q^{11} + 2\ q^{16} + q^{18} + q^{25} + q^{36} + q^{39} + q^{42} + q^{44} + 2\ q^{53} + q^{55} + q^{66} + q^{76} + q^{84}$
$F_{11} = 23 + 3\ q + 2\ q^{2} + q^{3} + 2\ q^{4} + q^{7} + q^{14} + 2\ q^{17} + q^{19} + q^{20} + q^{21} + q^{22} + q^{23} + q^{28} + q^{31} + q^{32} + q^{35} + q^{56} + q^{67} + q^{70} + q^{78} + q^{83} + q^{88} + q^{94} + q^{101} + q^{105} + q^{121} + q^{128} + q^{134}$
$F_{12} = 30 + 3\ q + 4\ q^{2} + q^{3} + 3\ q^{5} + q^{8} + 2\ q^{10} + q^{11} + q^{16} + 2\ q^{20} + q^{22} + q^{24} + q^{27} + q^{34} + q^{40} + q^{49} + q^{50} + q^{51} + 2\ q^{52} + q^{55} + q^{66} + 2\ q^{68} + q^{73} + q^{77} + q^{83} + 2\ q^{118} + q^{139} + q^{144} + q^{156} + q^{176} + q^{186} + q^{197} + q^{198} + q^{208} + q^{216} + q^{223}$
$F_{13} = 41 + 3\ q + q^{2} + 2\ q^{3} + 2\ q^{4} + q^{6} + 2\ q^{7} + 2\ q^{8} + 2\ q^{10} + q^{14} + q^{19} + q^{21} + 2\ q^{23} + q^{27} + q^{28} + 2\ q^{30} + q^{33} + q^{37} + q^{59} + q^{62} + q^{65} + q^{68} + q^{73} + q^{75} + q^{82} + q^{88} + q^{89} + q^{90} + q^{101} + q^{103} + q^{106} + q^{119} + q^{126} + q^{127} + q^{130} + q^{171} + q^{176} + q^{185} + q^{194} + q^{204} + q^{229} + q^{234} + q^{256} + q^{287} + q^{288} + q^{297} + q^{341} + 2\ q^{347} + q^{372} + q^{391} + q^{406}$
$F_{14} = 52 + 4\ q + 4\ q^{2} + 2\ q^{3} + q^{4} + 2\ q^{5} + 2\ q^{8} + 4\ q^{10} + q^{11} + q^{16} + 3\ q^{20} + 2\ q^{24} + q^{27} + q^{28} + q^{31} + 2\ q^{40} + q^{41} + q^{44} + q^{47} + q^{50} + q^{64} + q^{73} + q^{74} + q^{79} + 2\ q^{80} + q^{82} + q^{86} + q^{93} + q^{105} + q^{107} + q^{117} + q^{118} + q^{122} + q^{127} + q^{135} + q^{161} + q^{168} + q^{197} + q^{203} + q^{215} + q^{227} + q^{230} + q^{238} + q^{250} + q^{257} + q^{262} + q^{266} + q^{270} + q^{286} + q^{299} + q^{376} + q^{382} + q^{383} + q^{401} + q^{404} + q^{424} + q^{440} + q^{474} + q^{528} + q^{531} + q^{581} + q^{591} + q^{607} + q^{616} + q^{622} + q^{729} + q^{787}$
$F_{15} = 67 + 6\ q + 2\ q^{2} + 2\ q^{3} + 2\ q^{4} + 2\ q^{6} + q^{7} + 3\ q^{8} + 2\ q^{10} + 2\ q^{11} + q^{14} + q^{17} + q^{18} + 3\ q^{20} + q^{21} + 2\ q^{23} + q^{27} + 2\ q^{30} + q^{33} + q^{34} + q^{37} + q^{38} + q^{40} + q^{47} + q^{52} + q^{59} + q^{69} + q^{70} + q^{79} + q^{83} + q^{84} + q^{90} + q^{91} + q^{92} + q^{95} + q^{110} + q^{122} + q^{136} + q^{144} + 2\ q^{145} + q^{154} + q^{166} + q^{170} + q^{176} + q^{193} + q^{204} + q^{208} + q^{216} + q^{221} + q^{246} + q^{290} + q^{309} + q^{312} + q^{329} + q^{332} + q^{336} + q^{339} + q^{359} + q^{366} + q^{373} + q^{379} + q^{383} + q^{399} + q^{416} + q^{447} + 2\ q^{471} + q^{484} + q^{493} + q^{529} + q^{585} + q^{591} + q^{603} + q^{619} + q^{680} + q^{729} + q^{767} + q^{771} + q^{803} + 2\ q^{814} + q^{927} + q^{928} + q^{931} + q^{960} + q^{962} + q^{1013} + q^{1052} + q^{1194} + q^{1271} + q^{1300} + q^{1444}$
$F_{16} = 84 + 6\ q + 6\ q^{2} + 3\ q^{3} + 2\ q^{4} + 3\ q^{5} + 2\ q^{8} + q^{9} + 4\ q^{10} + 2\ q^{11} + q^{16} + q^{23} + 2\ q^{24} + 2\ q^{27} + 2\ q^{28} + q^{34} + q^{35} + 2\ q^{37} + q^{38} + q^{39} + q^{40} + q^{41} + 2\ q^{43} + 2\ q^{50} + q^{51} + q^{60} + q^{64} + q^{65} + q^{73} + q^{76} + q^{80} + q^{81} + q^{83} + q^{85} + q^{90} + q^{92} + q^{94} + q^{97} + q^{107} + q^{120} + q^{127} + q^{148} + q^{157} + q^{161} + q^{173} + q^{176} + q^{178} + q^{180} + q^{186} + q^{188} + q^{190} + q^{202} + q^{218} + q^{221} + q^{231} + q^{236} + q^{245} + q^{267} + q^{278} + q^{285} + q^{312} + q^{324} + q^{338} + q^{350} + q^{363} + q^{410} + q^{417} + q^{422} + q^{452} + q^{453} + q^{469} + q^{470} + q^{483} + q^{490} + q^{497} + q^{516} + q^{542} + q^{602} + q^{606} + q^{662} + q^{663} + q^{665} + q^{692} + q^{702} + q^{743} + q^{803} + q^{817} + q^{857} + q^{885} + q^{891} + q^{915} + q^{919} + q^{932} + q^{944} + q^{958} + q^{979} + q^{986} + q^{1015} + q^{1034} + q^{1067} + q^{1178} + q^{1208} + q^{1220} + q^{1267} + q^{1332} + q^{1384} + q^{1401} + q^{1496} + q^{1512} + 2\ q^{1526} + q^{1740} + q^{1800} + q^{1815} + q^{1893} + q^{1909} + q^{1988} + q^{2043} + q^{2105} + q^{2189} + q^{2557} + q^{2571}$
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions.
Code
def statistic(mu):
s = SymmetricFunctions(QQ).s()
F = species.PartitionSpecies().cycle_index_series()
return F.coefficient(mu.size()).scalar(s(mu))
Created
Sep 26, 2020 at 23:09 by Martin Rubey
Updated
Sep 26, 2020 at 23:09 by Martin Rubey
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