Identifier
Values
[3] => 1
[2,1] => 0
[1,1,1] => 0
[4] => 1
[3,1] => 0
[2,2] => 1
[2,1,1] => 0
[1,1,1,1] => 0
[5] => 1
[4,1] => 0
[3,2] => 1
[3,1,1] => 0
[2,2,1] => 1
[2,1,1,1] => 0
[1,1,1,1,1] => 1
[6] => 1
[5,1] => 0
[4,2] => 2
[4,1,1] => 0
[3,3] => 0
[3,2,1] => 1
[3,1,1,1] => 1
[2,2,2] => 2
[2,2,1,1] => 0
[2,1,1,1,1] => 1
[1,1,1,1,1,1] => 0
[7] => 1
[6,1] => 0
[5,2] => 2
[5,1,1] => 0
[4,3] => 1
[4,2,1] => 3
[4,1,1,1] => 1
[3,3,1] => 0
[3,2,2] => 3
[3,2,1,1] => 2
[3,1,1,1,1] => 3
[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] => 1
[7,1] => 0
[6,2] => 3
[6,1,1] => 0
[5,3] => 1
[5,2,1] => 4
[5,1,1,1] => 2
[4,4] => 3
[4,3,1] => 3
[4,2,2] => 7
[4,2,1,1] => 4
[4,1,1,1,1] => 4
[3,3,2] => 1
[3,3,1,1] => 5
[3,2,2,1] => 4
[3,2,1,1,1] => 4
[3,1,1,1,1,1] => 1
[2,2,2,2] => 3
[2,2,2,1,1] => 0
[2,2,1,1,1,1] => 2
[2,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1] => 0
[9] => 1
[8,1] => 0
[7,2] => 3
[7,1,1] => 0
[6,3] => 3
[6,2,1] => 6
[6,1,1,1] => 3
[5,4] => 3
[5,3,1] => 6
[5,2,2] => 11
[5,2,1,1] => 9
[5,1,1,1,1] => 7
[4,4,1] => 7
[4,3,2] => 9
[4,3,1,1] => 12
[4,2,2,1] => 12
[4,2,1,1,1] => 9
[4,1,1,1,1,1] => 3
[3,3,3] => 0
[3,3,2,1] => 9
[3,3,1,1,1] => 11
[3,2,2,2] => 7
[3,2,2,1,1] => 6
[3,2,1,1,1,1] => 6
[3,1,1,1,1,1,1] => 0
[2,2,2,2,1] => 3
[2,2,2,1,1,1] => 3
[2,2,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1] => 1
[10] => 1
[9,1] => 0
[8,2] => 4
[8,1,1] => 0
[7,3] => 3
[7,2,1] => 8
[7,1,1,1] => 4
[6,4] => 8
>>> Load all 1197 entries. <<<[6,3,1] => 13
[6,2,2] => 18
[6,2,1,1] => 14
[6,1,1,1,1] => 10
[5,5] => 0
[5,4,1] => 14
[5,3,2] => 20
[5,3,1,1] => 31
[5,2,2,1] => 26
[5,2,1,1,1] => 22
[5,1,1,1,1,1] => 6
[4,4,2] => 20
[4,4,1,1] => 10
[4,3,3] => 6
[4,3,2,1] => 38
[4,3,1,1,1] => 29
[4,2,2,2] => 22
[4,2,2,1,1] => 22
[4,2,1,1,1,1] => 20
[4,1,1,1,1,1,1] => 2
[3,3,3,1] => 12
[3,3,2,2] => 8
[3,3,2,1,1] => 26
[3,3,1,1,1,1] => 9
[3,2,2,2,1] => 14
[3,2,2,1,1,1] => 16
[3,2,1,1,1,1,1] => 8
[3,1,1,1,1,1,1,1] => 2
[2,2,2,2,2] => 6
[2,2,2,2,1,1] => 2
[2,2,2,1,1,1,1] => 6
[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] => 0
[11] => 1
[10,1] => 0
[9,2] => 4
[9,1,1] => 0
[8,3] => 5
[8,2,1] => 11
[8,1,1,1] => 5
[7,4] => 10
[7,3,1] => 20
[7,2,2] => 25
[7,2,1,1] => 24
[7,1,1,1,1] => 15
[6,5] => 6
[6,4,1] => 34
[6,3,2] => 45
[6,3,1,1] => 56
[6,2,2,1] => 50
[6,2,1,1,1] => 40
[6,1,1,1,1,1] => 11
[5,5,1] => 10
[5,4,2] => 50
[5,4,1,1] => 50
[5,3,3] => 20
[5,3,2,1] => 105
[5,3,1,1,1] => 80
[5,2,2,2] => 45
[5,2,2,1,1] => 60
[5,2,1,1,1,1] => 44
[5,1,1,1,1,1,1] => 5
[4,4,3] => 26
[4,4,2,1] => 60
[4,4,1,1,1] => 30
[4,3,3,1] => 54
[4,3,2,2] => 60
[4,3,2,1,1] => 105
[4,3,1,1,1,1] => 50
[4,2,2,2,1] => 55
[4,2,2,1,1,1] => 56
[4,2,1,1,1,1,1] => 30
[4,1,1,1,1,1,1,1] => 5
[3,3,3,2] => 16
[3,3,3,1,1] => 40
[3,3,2,2,1] => 40
[3,3,2,1,1,1] => 45
[3,3,1,1,1,1,1] => 10
[3,2,2,2,2] => 20
[3,2,2,2,1,1] => 29
[3,2,2,1,1,1,1] => 30
[3,2,1,1,1,1,1,1] => 10
[3,1,1,1,1,1,1,1,1] => 5
[2,2,2,2,2,1] => 6
[2,2,2,2,1,1,1] => 5
[2,2,2,1,1,1,1,1] => 5
[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] => 1
[11,1] => 0
[10,2] => 5
[10,1,1] => 0
[9,3] => 6
[9,2,1] => 13
[9,1,1,1] => 7
[8,4] => 17
[8,3,1] => 32
[8,2,2] => 37
[8,2,1,1] => 34
[8,1,1,1,1] => 19
[7,5] => 9
[7,4,1] => 59
[7,3,2] => 77
[7,3,1,1] => 102
[7,2,2,1] => 86
[7,2,1,1,1] => 72
[7,1,1,1,1,1] => 19
[6,6] => 12
[6,5,1] => 45
[6,4,2] => 128
[6,4,1,1] => 117
[6,3,3] => 56
[6,3,2,1] => 234
[6,3,1,1,1] => 163
[6,2,2,2] => 98
[6,2,2,1,1] => 132
[6,2,1,1,1,1] => 93
[6,1,1,1,1,1,1] => 14
[5,5,2] => 44
[5,5,1,1] => 71
[5,4,3] => 87
[5,4,2,1] => 241
[5,4,1,1,1] => 146
[5,3,3,1] => 177
[5,3,2,2] => 176
[5,3,2,1,1] => 327
[5,3,1,1,1,1] => 144
[5,2,2,2,1] => 146
[5,2,2,1,1,1] => 155
[5,2,1,1,1,1,1] => 72
[5,1,1,1,1,1,1,1] => 14
[4,4,4] => 32
[4,4,3,1] => 117
[4,4,2,2] => 133
[4,4,2,1,1] => 169
[4,4,1,1,1,1] => 90
[4,3,3,2] => 113
[4,3,3,1,1] => 187
[4,3,2,2,1] => 238
[4,3,2,1,1,1] => 234
[4,3,1,1,1,1,1] => 82
[4,2,2,2,2] => 79
[4,2,2,2,1,1] => 117
[4,2,2,1,1,1,1] => 110
[4,2,1,1,1,1,1,1] => 36
[4,1,1,1,1,1,1,1,1] => 10
[3,3,3,3] => 26
[3,3,3,2,1] => 87
[3,3,3,1,1,1] => 66
[3,3,2,2,2] => 44
[3,3,2,2,1,1] => 121
[3,3,2,1,1,1,1] => 74
[3,3,1,1,1,1,1,1] => 29
[3,2,2,2,2,1] => 47
[3,2,2,2,1,1,1] => 59
[3,2,2,1,1,1,1,1] => 37
[3,2,1,1,1,1,1,1,1] => 13
[3,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2] => 12
[2,2,2,2,2,1,1] => 7
[2,2,2,2,1,1,1,1] => 14
[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] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[13] => 1
[12,1] => 0
[11,2] => 5
[11,1,1] => 0
[10,3] => 8
[10,2,1] => 17
[10,1,1,1] => 8
[9,4] => 21
[9,3,1] => 45
[9,2,2] => 48
[9,2,1,1] => 50
[9,1,1,1,1] => 27
[8,5] => 22
[8,4,1] => 102
[8,3,2] => 132
[8,3,1,1] => 162
[8,2,2,1] => 140
[8,2,1,1,1] => 113
[8,1,1,1,1,1] => 30
[7,6] => 19
[7,5,1] => 100
[7,4,2] => 246
[7,4,1,1] => 256
[7,3,3] => 115
[7,3,2,1] => 462
[7,3,1,1,1] => 320
[7,2,2,2] => 172
[7,2,2,1,1] => 261
[7,2,1,1,1,1] => 170
[7,1,1,1,1,1,1] => 26
[6,6,1] => 57
[6,5,2] => 198
[6,5,1,1] => 220
[6,4,3] => 255
[6,4,2,1] => 660
[6,4,1,1,1] => 384
[6,3,3,1] => 440
[6,3,2,2] => 462
[6,3,2,1,1] => 792
[6,3,1,1,1,1] => 360
[6,2,2,2,1] => 351
[6,2,2,1,1,1] => 360
[6,2,1,1,1,1,1] => 170
[6,1,1,1,1,1,1,1] => 30
[5,5,3] => 112
[5,5,2,1] => 330
[5,5,1,1,1] => 215
[5,4,4] => 114
[5,4,3,1] => 575
[5,4,2,2] => 510
[5,4,2,1,1] => 810
[5,4,1,1,1,1] => 351
[5,3,3,2] => 423
[5,3,3,1,1] => 656
[5,3,2,2,1] => 810
[5,3,2,1,1,1] => 792
[5,3,1,1,1,1,1] => 261
[5,2,2,2,2] => 215
[5,2,2,2,1,1] => 384
[5,2,2,1,1,1,1] => 320
[5,2,1,1,1,1,1,1] => 113
[5,1,1,1,1,1,1,1,1] => 27
[4,4,4,1] => 132
[4,4,3,2] => 340
[4,4,3,1,1] => 423
[4,4,2,2,1] => 510
[4,4,2,1,1,1] => 462
[4,4,1,1,1,1,1] => 172
[4,3,3,3] => 132
[4,3,3,2,1] => 575
[4,3,3,1,1,1] => 440
[4,3,2,2,2] => 330
[4,3,2,2,1,1] => 660
[4,3,2,1,1,1,1] => 462
[4,3,1,1,1,1,1,1] => 140
[4,2,2,2,2,1] => 220
[4,2,2,2,1,1,1] => 256
[4,2,2,1,1,1,1,1] => 162
[4,2,1,1,1,1,1,1,1] => 50
[4,1,1,1,1,1,1,1,1,1] => 8
[3,3,3,3,1] => 114
[3,3,3,2,2] => 112
[3,3,3,2,1,1] => 255
[3,3,3,1,1,1,1] => 115
[3,3,2,2,2,1] => 198
[3,3,2,2,1,1,1] => 246
[3,3,2,1,1,1,1,1] => 132
[3,3,1,1,1,1,1,1,1] => 48
[3,2,2,2,2,2] => 57
[3,2,2,2,2,1,1] => 100
[3,2,2,2,1,1,1,1] => 102
[3,2,2,1,1,1,1,1,1] => 45
[3,2,1,1,1,1,1,1,1,1] => 17
[3,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,1] => 19
[2,2,2,2,2,1,1,1] => 22
[2,2,2,2,1,1,1,1,1] => 21
[2,2,2,1,1,1,1,1,1,1] => 8
[2,2,1,1,1,1,1,1,1,1,1] => 5
[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] => 1
[14] => 1
[13,1] => 0
[12,2] => 6
[12,1,1] => 0
[11,3] => 9
[11,2,1] => 20
[11,1,1,1] => 10
[10,4] => 31
[10,3,1] => 64
[10,2,2] => 65
[10,2,1,1] => 66
[10,1,1,1,1] => 34
[9,5] => 32
[9,4,1] => 156
[9,3,2] => 201
[9,3,1,1] => 254
[9,2,2,1] => 214
[9,2,1,1,1] => 176
[9,1,1,1,1,1] => 45
[8,6] => 47
[8,5,1] => 207
[8,4,2] => 462
[8,4,1,1] => 465
[8,3,3] => 221
[8,3,2,1] => 832
[8,3,1,1,1] => 555
[8,2,2,2] => 306
[8,2,2,1,1] => 468
[8,2,1,1,1,1] => 300
[8,1,1,1,1,1,1] => 51
[7,7] => 7
[7,6,1] => 163
[7,5,2] => 483
[7,5,1,1] => 567
[7,4,3] => 572
[7,4,2,1] => 1501
[7,4,1,1,1] => 891
[7,3,3,1] => 972
[7,3,2,2] => 986
[7,3,2,1,1] => 1715
[7,3,1,1,1,1] => 759
[7,2,2,2,1] => 728
[7,2,2,1,1,1] => 752
[7,2,1,1,1,1,1] => 339
[7,1,1,1,1,1,1,1] => 62
[6,6,2] => 264
[6,6,1,1] => 224
[6,5,3] => 520
[6,5,2,1] => 1307
[6,5,1,1,1] => 762
[6,4,4] => 363
[6,4,3,1] => 1770
[6,4,2,2] => 1569
[6,4,2,1,1] => 2433
[6,4,1,1,1,1] => 1050
[6,3,3,2] => 1210
[6,3,3,1,1] => 1768
[6,3,2,2,1] => 2241
[6,3,2,1,1,1] => 2139
[6,3,1,1,1,1,1] => 732
[6,2,2,2,2] => 550
[6,2,2,2,1,1] => 990
[6,2,2,1,1,1,1] => 799
[6,2,1,1,1,1,1,1] => 280
[6,1,1,1,1,1,1,1,1] => 54
[5,5,4] => 192
[5,5,3,1] => 984
[5,5,2,2] => 714
[5,5,2,1,1] => 1285
[5,5,1,1,1,1] => 478
[5,4,4,1] => 747
[5,4,3,2] => 1716
[5,4,3,1,1] => 2288
[5,4,2,2,1] => 2451
[5,4,2,1,1,1] => 2253
[5,4,1,1,1,1,1] => 728
[5,3,3,3] => 555
[5,3,3,2,1] => 2288
[5,3,3,1,1,1] => 1704
[5,3,2,2,2] => 1225
[5,3,2,2,1,1] => 2505
[5,3,2,1,1,1,1] => 1695
[5,3,1,1,1,1,1,1] => 508
[5,2,2,2,2,1] => 750
[5,2,2,2,1,1,1] => 891
[5,2,2,1,1,1,1,1] => 535
[5,2,1,1,1,1,1,1,1] => 176
[5,1,1,1,1,1,1,1,1,1] => 25
[4,4,4,2] => 474
[4,4,4,1,1] => 495
[4,4,3,3] => 394
[4,4,3,2,1] => 1716
[4,4,3,1,1,1] => 1270
[4,4,2,2,2] => 834
[4,4,2,2,1,1] => 1449
[4,4,2,1,1,1,1] => 1034
[4,4,1,1,1,1,1,1] => 258
[4,3,3,3,1] => 767
[4,3,3,2,2] => 924
[4,3,3,2,1,1] => 1810
[4,3,3,1,1,1,1] => 936
[4,3,2,2,2,1] => 1307
[4,3,2,2,1,1,1] => 1509
[4,3,2,1,1,1,1,1] => 832
[4,3,1,1,1,1,1,1,1] => 222
[4,2,2,2,2,2] => 284
[4,2,2,2,2,1,1] => 519
[4,2,2,2,1,1,1,1] => 505
[4,2,2,1,1,1,1,1,1] => 234
[4,2,1,1,1,1,1,1,1,1] => 78
[4,1,1,1,1,1,1,1,1,1,1] => 7
[3,3,3,3,2] => 232
[3,3,3,3,1,1] => 303
[3,3,3,2,2,1] => 540
[3,3,3,2,1,1,1] => 572
[3,3,3,1,1,1,1,1] => 257
[3,3,2,2,2,2] => 204
[3,3,2,2,2,1,1] => 523
[3,3,2,2,1,1,1,1] => 414
[3,3,2,1,1,1,1,1,1] => 213
[3,3,1,1,1,1,1,1,1,1] => 45
[3,2,2,2,2,2,1] => 163
[3,2,2,2,2,1,1,1] => 215
[3,2,2,2,1,1,1,1,1] => 156
[3,2,2,1,1,1,1,1,1,1] => 72
[3,2,1,1,1,1,1,1,1,1,1] => 20
[3,1,1,1,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,2,2] => 27
[2,2,2,2,2,2,1,1] => 27
[2,2,2,2,2,1,1,1,1] => 44
[2,2,2,2,1,1,1,1,1,1] => 19
[2,2,2,1,1,1,1,1,1,1,1] => 13
[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] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[15] => 1
[14,1] => 0
[13,2] => 6
[13,1,1] => 0
[12,3] => 12
[12,2,1] => 24
[12,1,1,1] => 12
[11,4] => 37
[11,3,1] => 84
[11,2,2] => 82
[11,2,1,1] => 90
[11,1,1,1,1] => 44
[10,5] => 55
[10,4,1] => 237
[10,3,2] => 303
[10,3,1,1] => 370
[10,2,2,1] => 315
[10,2,1,1,1] => 254
[10,1,1,1,1,1] => 67
[9,6] => 74
[9,5,1] => 361
[9,4,2] => 769
[9,4,1,1] => 817
[9,3,3] => 384
[9,3,2,1] => 1400
[9,3,1,1,1] => 934
[9,2,2,2] => 491
[9,2,2,1,1] => 790
[9,2,1,1,1,1] => 486
[9,1,1,1,1,1,1] => 83
[8,7] => 47
[8,6,1] => 397
[8,5,2] => 1068
[8,5,1,1] => 1170
[8,4,3] => 1177
[8,4,2,1] => 3034
[8,4,1,1,1] => 1769
[8,3,3,1] => 1911
[8,3,2,2] => 1966
[8,3,2,1,1] => 3337
[8,3,1,1,1,1] => 1485
[8,2,2,2,1] => 1407
[8,2,2,1,1,1] => 1438
[8,2,1,1,1,1,1] => 651
[8,1,1,1,1,1,1,1] => 114
[7,7,1] => 150
[7,6,2] => 851
[7,6,1,1] => 890
[7,5,3] => 1449
[7,5,2,1] => 3604
[7,5,1,1,1] => 2100
[7,4,4] => 888
[7,4,3,1] => 4494
[7,4,2,2] => 3792
[7,4,2,1,1] => 6090
[7,4,1,1,1,1] => 2521
[7,3,3,2] => 2940
[7,3,3,1,1] => 4200
[7,3,2,2,1] => 5274
[7,3,2,1,1,1] => 5004
[7,3,1,1,1,1,1] => 1680
[7,2,2,2,2] => 1210
[7,2,2,2,1,1] => 2301
[7,2,2,1,1,1,1] => 1785
[7,2,1,1,1,1,1,1] => 636
[7,1,1,1,1,1,1,1,1] => 118
[6,6,3] => 752
[6,6,2,1] => 1667
[6,6,1,1,1] => 894
[6,5,4] => 999
[6,5,3,1] => 4290
[6,5,2,2] => 3338
[6,5,2,1,1] => 5405
[6,5,1,1,1,1] => 2122
[6,4,4,1] => 2670
[6,4,3,2] => 5856
[6,4,3,1,1] => 7680
[6,4,2,2,1] => 8140
[6,4,2,1,1,1] => 7371
[6,4,1,1,1,1,1] => 2371
[6,3,3,3] => 1671
[6,3,3,2,1] => 6998
[6,3,3,1,1,1] => 5202
[6,3,2,2,2] => 3738
[6,3,2,2,1,1] => 7371
[6,3,2,1,1,1,1] => 5004
[6,3,1,1,1,1,1,1] => 1438
[6,2,2,2,2,1] => 2122
[6,2,2,2,1,1,1] => 2486
[6,2,2,1,1,1,1,1] => 1485
[6,2,1,1,1,1,1,1,1] => 466
[6,1,1,1,1,1,1,1,1,1] => 67
[5,5,5] => 168
[5,5,4,1] => 1801
[5,5,3,2] => 3165
[5,5,3,1,1] => 4310
[5,5,2,2,1] => 4117
[5,5,2,1,1,1] => 3738
[5,5,1,1,1,1,1] => 1084
[5,4,4,2] => 2756
[5,4,4,1,1] => 3266
[5,4,3,3] => 2483
[5,4,3,2,1] => 9764
[5,4,3,1,1,1] => 7012
[5,4,2,2,2] => 4222
[5,4,2,2,1,1] => 8077
[5,4,2,1,1,1,1] => 5344
[5,4,1,1,1,1,1,1] => 1393
[5,3,3,3,1] => 3406
[5,3,3,2,2] => 4100
[5,3,3,2,1,1] => 7764
[5,3,3,1,1,1,1] => 3990
[5,3,2,2,2,1] => 5405
[5,3,2,2,1,1,1] => 6195
[5,3,2,1,1,1,1,1] => 3337
[5,3,1,1,1,1,1,1,1] => 874
[5,2,2,2,2,2] => 978
[5,2,2,2,2,1,1] => 1995
[5,2,2,2,1,1,1,1] => 1804
[5,2,2,1,1,1,1,1,1] => 864
[5,2,1,1,1,1,1,1,1,1] => 260
[5,1,1,1,1,1,1,1,1,1,1] => 23
[4,4,4,3] => 802
[4,4,4,2,1] => 2518
[4,4,4,1,1,1] => 1671
[4,4,3,3,1] => 2651
[4,4,3,2,2] => 3270
[4,4,3,2,1,1] => 5821
[4,4,3,1,1,1,1] => 3066
[4,4,2,2,2,1] => 3338
[4,4,2,2,1,1,1] => 3680
[4,4,2,1,1,1,1,1] => 1966
[4,4,1,1,1,1,1,1,1] => 421
[4,3,3,3,2] => 1801
[4,3,3,3,1,1] => 2670
[4,3,3,2,2,1] => 4290
[4,3,3,2,1,1,1] => 4515
[4,3,3,1,1,1,1,1] => 1911
[4,3,2,2,2,2] => 1667
[4,3,2,2,2,1,1] => 3604
[4,3,2,2,1,1,1,1] => 3034
[4,3,2,1,1,1,1,1,1] => 1400
[4,3,1,1,1,1,1,1,1,1] => 315
[4,2,2,2,2,2,1] => 911
[4,2,2,2,2,1,1,1] => 1170
[4,2,2,2,1,1,1,1,1] => 852
[4,2,2,1,1,1,1,1,1,1] => 370
[4,2,1,1,1,1,1,1,1,1,1] => 105
[4,1,1,1,1,1,1,1,1,1,1,1] => 12
[3,3,3,3,3] => 238
[3,3,3,3,2,1] => 999
[3,3,3,3,1,1,1] => 783
[3,3,3,2,2,2] => 682
[3,3,3,2,2,1,1] => 1554
[3,3,3,2,1,1,1,1] => 1156
[3,3,3,1,1,1,1,1,1] => 468
[3,3,2,2,2,2,1] => 816
[3,3,2,2,2,1,1,1] => 1068
[3,3,2,2,1,1,1,1,1] => 706
[3,3,2,1,1,1,1,1,1,1] => 303
[3,3,1,1,1,1,1,1,1,1,1] => 47
[3,2,2,2,2,2,2] => 185
[3,2,2,2,2,2,1,1] => 376
[3,2,2,2,2,1,1,1,1] => 396
[3,2,2,2,1,1,1,1,1,1] => 230
[3,2,2,1,1,1,1,1,1,1,1] => 105
[3,2,1,1,1,1,1,1,1,1,1,1] => 23
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 7
[2,2,2,2,2,2,2,1] => 47
[2,2,2,2,2,2,1,1,1] => 60
[2,2,2,2,2,1,1,1,1,1] => 55
[2,2,2,2,1,1,1,1,1,1,1] => 23
[2,2,2,1,1,1,1,1,1,1,1,1] => 12
[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] => 1
[15,1] => 0
[14,2] => 7
[14,1,1] => 0
[13,3] => 13
[13,2,1] => 28
[13,1,1,1] => 14
[12,4] => 51
[12,3,1] => 111
[12,2,2] => 105
[12,2,1,1] => 114
[12,1,1,1,1] => 54
[11,5] => 75
[11,4,1] => 336
[11,3,2] => 429
[11,3,1,1] => 531
[11,2,2,1] => 446
[11,2,1,1,1] => 364
[11,1,1,1,1,1] => 93
[10,6] => 133
[10,5,1] => 611
[10,4,2] => 1251
[10,4,1,1] => 1309
[10,3,3] => 630
[10,3,2,1] => 2240
[10,3,1,1,1] => 1464
[10,2,2,2] => 779
[10,2,2,1,1] => 1260
[10,2,1,1,1,1] => 770
[10,1,1,1,1,1,1] => 138
[9,7] => 95
[9,6,1] => 780
[9,5,2] => 2023
[9,5,1,1] => 2256
[9,4,3] => 2184
[9,4,2,1] => 5630
[9,4,1,1,1] => 3300
[9,3,3,1] => 3514
[9,3,2,2] => 3561
[9,3,2,1,1] => 6076
[9,3,1,1,1,1] => 2670
[9,2,2,2,1] => 2520
[9,2,2,1,1,1] => 2576
[9,2,1,1,1,1,1] => 1144
[9,1,1,1,1,1,1,1] => 202
[8,8] => 65
[8,7,1] => 555
[8,6,2] => 2222
[8,6,1,1] => 2245
[8,5,3] => 3451
[8,5,2,1] => 8320
[8,5,1,1,1] => 4729
[8,4,4] => 1980
[8,4,3,1] => 9913
[8,4,2,2] => 8344
[8,4,2,1,1] => 13293
[8,4,1,1,1,1] => 5473
[8,3,3,2] => 6348
[8,3,3,1,1] => 8890
[8,3,2,2,1] => 11231
[8,3,2,1,1,1] => 10560
[8,3,1,1,1,1,1] => 3572
[8,2,2,2,2] => 2503
[8,2,2,2,1,1] => 4774
[8,2,2,1,1,1,1] => 3650
[8,2,1,1,1,1,1,1] => 1294
[8,1,1,1,1,1,1,1,1] => 220
[7,7,2] => 880
[7,7,1,1] => 1050
[7,6,3] => 2860
[7,6,2,1] => 6568
[7,6,1,1,1] => 3640
[7,5,4] => 3088
[7,5,3,1] => 13071
[7,5,2,2] => 9912
[7,5,2,1,1] => 16183
[7,5,1,1,1,1] => 6213
[7,4,4,1] => 7497
[7,4,3,2] => 16016
[7,4,3,1,1] => 21060
[7,4,2,2,1] => 21840
[7,4,2,1,1,1] => 19709
[7,4,1,1,1,1,1] => 6160
[7,3,3,3] => 4418
[7,3,3,2,1] => 18200
[7,3,3,1,1,1] => 13380
[7,3,2,2,2] => 9506
[7,3,2,2,1,1] => 18813
[7,3,2,1,1,1,1] => 12613
[7,3,1,1,1,1,1,1] => 3590
[7,2,2,2,2,1] => 5253
[7,2,2,2,1,1,1] => 6160
[7,2,2,1,1,1,1,1] => 3617
[7,2,1,1,1,1,1,1,1] => 1144
[7,1,1,1,1,1,1,1,1,1] => 155
[6,6,4] => 1705
[6,6,3,1] => 6195
[6,6,2,2] => 4870
[6,6,2,1,1] => 7392
[6,6,1,1,1,1] => 2940
[6,5,5] => 1070
[6,5,4,1] => 9152
[6,5,3,2] => 15583
[6,5,3,1,1] => 20349
[6,5,2,2,1] => 19685
[6,5,2,1,1,1] => 17472
[6,5,1,1,1,1,1] => 5225
[6,4,4,2] => 10703
[6,4,4,1,1] => 12688
[6,4,3,3] => 9267
[6,4,3,2,1] => 36036
[6,4,3,1,1,1] => 25655
[6,4,2,2,2] => 15246
[6,4,2,2,1,1] => 28846
[6,4,2,1,1,1,1] => 18883
[6,4,1,1,1,1,1,1] => 4802
[6,3,3,3,1] => 11340
[6,3,3,2,2] => 13832
[6,3,3,2,1,1] => 25690
[6,3,3,1,1,1,1] => 13275
[6,3,2,2,2,1] => 17472
[6,3,2,2,1,1,1] => 19744
[6,3,2,1,1,1,1,1] => 10560
[6,3,1,1,1,1,1,1,1] => 2608
[6,2,2,2,2,2] => 2982
[6,2,2,2,2,1,1] => 6143
[6,2,2,2,1,1,1,1] => 5473
[6,2,2,1,1,1,1,1,1] => 2625
[6,2,1,1,1,1,1,1,1,1] => 763
[6,1,1,1,1,1,1,1,1,1,1] => 83
[5,5,5,1] => 1898
[5,5,4,2] => 7122
[5,5,4,1,1] => 8855
[5,5,3,3] => 5485
[5,5,3,2,1] => 20020
[5,5,3,1,1,1] => 13944
[5,5,2,2,2] => 7643
[5,5,2,2,1,1] => 15162
[5,5,2,1,1,1,1] => 9478
[5,5,1,1,1,1,1,1] => 2433
[5,4,4,3] => 5608
[5,4,4,2,1] => 17160
[5,4,4,1,1,1] => 11277
[5,4,3,3,1] => 17160
[5,4,3,2,2] => 20020
[5,4,3,2,1,1] => 36036
[5,4,3,1,1,1,1] => 18200
[5,4,2,2,2,1] => 19706
[5,4,2,2,1,1,1] => 21840
[5,4,2,1,1,1,1,1] => 11259
[5,4,1,1,1,1,1,1,1] => 2520
[5,3,3,3,2] => 8820
[5,3,3,3,1,1] => 12800
[5,3,3,2,2,1] => 20286
[5,3,3,2,1,1,1] => 21060
[5,3,3,1,1,1,1,1] => 8785
[5,3,2,2,2,2] => 7434
[5,3,2,2,2,1,1] => 16183
[5,3,2,2,1,1,1,1] => 13363
[5,3,2,1,1,1,1,1,1] => 6083
[5,3,1,1,1,1,1,1,1,1] => 1305
[5,2,2,2,2,2,1] => 3640
[5,2,2,2,2,1,1,1] => 4694
[5,2,2,2,1,1,1,1,1] => 3300
[5,2,2,1,1,1,1,1,1,1] => 1432
[5,2,1,1,1,1,1,1,1,1,1] => 364
[5,1,1,1,1,1,1,1,1,1,1,1] => 43
[4,4,4,4] => 831
[4,4,4,3,1] => 5573
[4,4,4,2,2] => 5555
[4,4,4,2,1,1] => 9267
[4,4,4,1,1,1,1] => 4481
[4,4,3,3,2] => 7122
[4,4,3,3,1,1] => 10633
[4,4,3,2,2,1] => 15618
[4,4,3,2,1,1,1] => 16016
[4,4,3,1,1,1,1,1] => 6411
[4,4,2,2,2,2] => 4870
[4,4,2,2,2,1,1] => 9856
[4,4,2,2,1,1,1,1] => 8288
[4,4,2,1,1,1,1,1,1] => 3526
[4,4,1,1,1,1,1,1,1,1] => 744
[4,3,3,3,3] => 1933
[4,3,3,3,2,1] => 9152
[4,3,3,3,1,1,1] => 7455
[4,3,3,2,2,2] => 6160
[4,3,3,2,2,1,1] => 13134
[4,3,3,2,1,1,1,1] => 9913
[4,3,3,1,1,1,1,1,1] => 3556
[4,3,2,2,2,2,1] => 6561
[4,3,2,2,2,1,1,1] => 8320
[4,3,2,2,1,1,1,1,1] => 5616
[4,3,2,1,1,1,1,1,1,1] => 2240
[4,3,1,1,1,1,1,1,1,1,1] => 436
[4,2,2,2,2,2,2] => 1078
[4,2,2,2,2,2,1,1] => 2245
[4,2,2,2,2,1,1,1,1] => 2291
[4,2,2,2,1,1,1,1,1,1] => 1323
[4,2,2,1,1,1,1,1,1,1,1] => 549
[4,2,1,1,1,1,1,1,1,1,1,1] => 121
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 18
[3,3,3,3,3,1] => 1105
[3,3,3,3,2,2] => 1670
[3,3,3,3,2,1,1] => 3088
[3,3,3,3,1,1,1,1] => 1917
[3,3,3,2,2,2,1] => 2860
[3,3,3,2,2,1,1,1] => 3493
[3,3,3,2,1,1,1,1,1] => 2184
[3,3,3,1,1,1,1,1,1,1] => 672
[3,3,2,2,2,2,2] => 880
[3,3,2,2,2,2,1,1] => 2194
[3,3,2,2,2,1,1,1,1] => 2009
[3,3,2,2,1,1,1,1,1,1] => 1216
[3,3,2,1,1,1,1,1,1,1,1] => 422
[3,3,1,1,1,1,1,1,1,1,1,1] => 87
[3,2,2,2,2,2,2,1] => 562
[3,2,2,2,2,2,1,1,1] => 780
[3,2,2,2,2,1,1,1,1,1] => 625
[3,2,2,2,1,1,1,1,1,1,1] => 336
[3,2,2,1,1,1,1,1,1,1,1,1] => 121
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 28
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 3
[2,2,2,2,2,2,2,2] => 65
[2,2,2,2,2,2,2,1,1] => 88
[2,2,2,2,2,2,1,1,1,1] => 126
[2,2,2,2,2,1,1,1,1,1,1] => 68
[2,2,2,2,1,1,1,1,1,1,1,1] => 44
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 10
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 4
[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] => 1
[16,1] => 0
[15,2] => 7
[15,1,1] => 0
[14,3] => 16
[14,2,1] => 33
[14,1,1,1] => 16
[13,4] => 60
[13,3,1] => 140
[13,2,2] => 128
[13,2,1,1] => 147
[13,1,1,1,1] => 68
[12,5] => 112
[12,4,1] => 472
[12,3,2] => 600
[12,3,1,1] => 728
[12,2,2,1] => 616
[12,2,1,1,1] => 497
[12,1,1,1,1,1] => 128
[11,6] => 196
[11,5,1] => 952
[11,4,2] => 1904
[11,4,1,1] => 2048
[11,3,3] => 980
[11,3,2,1] => 3432
[11,3,1,1,1] => 2240
[11,2,2,2] => 1160
[11,2,2,1,1] => 1932
[11,2,1,1,1,1] => 1155
[11,1,1,1,1,1,1] => 208
[10,7] => 208
[10,6,1] => 1444
[10,5,2] => 3640
[10,5,1,1] => 3960
[10,4,3] => 3836
[10,4,2,1] => 9800
[10,4,1,1,1] => 5696
[10,3,3,1] => 6048
[10,3,2,2] => 6160
[10,3,2,1,1] => 10400
[10,3,1,1,1,1] => 4576
[10,2,2,2,1] => 4300
[10,2,2,1,1,1] => 4368
[10,2,1,1,1,1,1] => 1941
[10,1,1,1,1,1,1,1] => 336
[9,8] => 150
[9,7,1] => 1330
[9,6,2] => 4736
[9,6,1,1] => 4970
[9,5,3] => 7168
[9,5,2,1] => 17160
[9,5,1,1,1] => 9730
[9,4,4] => 3948
[9,4,3,1] => 19992
[9,4,2,2] => 16520
[9,4,2,1,1] => 26604
[9,4,1,1,1,1] => 10770
[9,3,3,2] => 12600
[9,3,3,1,1] => 17472
[9,3,2,2,1] => 21980
[9,3,2,1,1,1] => 20592
[9,3,1,1,1,1,1] => 6902
[9,2,2,2,2] => 4760
[9,2,2,2,1,1] => 9280
[9,2,2,1,1,1,1] => 6976
[9,2,1,1,1,1,1,1] => 2485
[9,1,1,1,1,1,1,1,1] => 414
[8,8,1] => 600
[8,7,2] => 3432
[8,7,1,1] => 3640
[8,6,3] => 8064
[8,6,2,1] => 18200
[8,6,1,1,1] => 9940
[8,5,4] => 8008
[8,5,3,1] => 32760
[8,5,2,2] => 24960
[8,5,2,1,1] => 40040
[8,5,1,1,1,1] => 15400
[8,4,4,1] => 18200
[8,4,3,2] => 38248
[8,4,3,1,1] => 49980
[8,4,2,2,1] => 51536
[8,4,2,1,1,1] => 46200
[8,4,1,1,1,1,1] => 14360
[8,3,3,3] => 10192
[8,3,3,2,1] => 42028
[8,3,3,1,1,1] => 30800
[8,3,2,2,2] => 21840
[8,3,2,2,1,1] => 42768
[8,3,2,1,1,1,1] => 28600
[8,3,1,1,1,1,1,1] => 8008
[8,2,2,2,2,1] => 11760
[8,2,2,2,1,1,1] => 13696
[8,2,2,1,1,1,1,1] => 8008
[8,2,1,1,1,1,1,1,1] => 2485
[8,1,1,1,1,1,1,1,1,1] => 336
[7,7,3] => 3470
[7,7,2,1] => 8008
[7,7,1,1,1] => 4480
[7,6,4] => 7220
[7,6,3,1] => 27006
[7,6,2,2] => 20104
[7,6,2,1,1] => 31780
[7,6,1,1,1,1] => 12040
[7,5,5] => 3864
[7,5,4,1] => 30888
[7,5,3,2] => 51312
[7,5,3,1,1] => 66654
[7,5,2,2,1] => 63560
[7,5,2,1,1,1] => 56056
[7,5,1,1,1,1,1] => 16464
[7,4,4,2] => 32256
[7,4,4,1,1] => 38720
[7,4,3,3] => 27944
[7,4,3,2,1] => 106496
[7,4,3,1,1,1] => 75110
[7,4,2,2,2] => 43904
[7,4,2,2,1,1] => 83944
[7,4,2,1,1,1,1] => 54040
[7,4,1,1,1,1,1,1] => 13696
[7,3,3,3,1] => 32060
[7,3,3,2,2] => 38976
[7,3,3,2,1,1] => 71640
[7,3,3,1,1,1,1] => 36810
[7,3,2,2,2,1] => 48048
[7,3,2,2,1,1,1] => 54040
[7,3,2,1,1,1,1,1] => 28600
[7,3,1,1,1,1,1,1,1] => 6976
[7,2,2,2,2,2] => 7784
[7,2,2,2,2,1,1] => 16464
[7,2,2,2,1,1,1,1] => 14360
[7,2,2,1,1,1,1,1,1] => 6902
[7,2,1,1,1,1,1,1,1,1] => 1941
[7,1,1,1,1,1,1,1,1,1,1] => 208
[6,6,5] => 2644
[6,6,4,1] => 16016
[6,6,3,2] => 25130
[6,6,3,1,1] => 31808
[6,6,2,2,1] => 30156
[6,6,2,1,1,1] => 26208
[6,6,1,1,1,1,1] => 7784
[6,5,5,1] => 11440
[6,5,4,2] => 40040
[6,5,4,1,1] => 48048
[6,5,3,3] => 28600
[6,5,3,2,1] => 105098
[6,5,3,1,1,1] => 72800
[6,5,2,2,2] => 40040
[6,5,2,2,1,1] => 76440
[6,5,2,1,1,1,1] => 48048
[6,5,1,1,1,1,1,1] => 11760
[6,4,4,3] => 24024
[6,4,4,2,1] => 72128
[6,4,4,1,1,1] => 46800
[6,4,3,3,1] => 69372
[6,4,3,2,2] => 80192
[6,4,3,2,1,1] => 143290
[6,4,3,1,1,1,1] => 71640
[6,4,2,2,2,1] => 76440
[6,4,2,2,1,1,1] => 83944
[6,4,2,1,1,1,1,1] => 42768
[6,4,1,1,1,1,1,1,1] => 9280
[6,3,3,3,2] => 32032
[6,3,3,3,1,1] => 46800
[6,3,3,2,2,1] => 72800
[6,3,3,2,1,1,1] => 75110
[6,3,3,1,1,1,1,1] => 30800
[6,3,2,2,2,2] => 26208
[6,3,2,2,2,1,1] => 56056
[6,3,2,2,1,1,1,1] => 46200
[6,3,2,1,1,1,1,1,1] => 20592
[6,3,1,1,1,1,1,1,1,1] => 4368
[6,2,2,2,2,2,1] => 12040
[6,2,2,2,2,1,1,1] => 15400
[6,2,2,2,1,1,1,1,1] => 10770
[6,2,2,1,1,1,1,1,1,1] => 4576
[6,2,1,1,1,1,1,1,1,1,1] => 1155
[6,1,1,1,1,1,1,1,1,1,1,1] => 128
[5,5,5,2] => 8440
[5,5,5,1,1] => 10220
[5,5,4,3] => 17160
[5,5,4,2,1] => 49980
[5,5,4,1,1,1] => 32032
[5,5,3,3,1] => 40320
[5,5,3,2,2] => 44730
[5,5,3,2,1,1] => 80192
[5,5,3,1,1,1,1] => 38976
[5,5,2,2,2,1] => 40040
[5,5,2,2,1,1,1] => 43904
[5,5,2,1,1,1,1,1] => 21840
[5,5,1,1,1,1,1,1,1] => 4760
[5,4,4,4] => 6076
[5,4,4,3,1] => 42760
[5,4,4,2,2] => 40320
[5,4,4,2,1,1] => 69372
[5,4,4,1,1,1,1] => 32060
[5,4,3,3,2] => 49980
[5,4,3,3,1,1] => 72128
[5,4,3,2,2,1] => 105098
[5,4,3,2,1,1,1] => 106496
[5,4,3,1,1,1,1,1] => 42028
[5,4,2,2,2,2] => 30156
[5,4,2,2,2,1,1] => 63560
[5,4,2,2,1,1,1,1] => 51536
[5,4,2,1,1,1,1,1,1] => 21980
[5,4,1,1,1,1,1,1,1,1] => 4300
[5,3,3,3,3] => 10220
[5,3,3,3,2,1] => 48048
[5,3,3,3,1,1,1] => 38720
[5,3,3,2,2,2] => 31808
[5,3,3,2,2,1,1] => 66654
[5,3,3,2,1,1,1,1] => 49980
[5,3,3,1,1,1,1,1,1] => 17472
[5,3,2,2,2,2,1] => 31780
[5,3,2,2,2,1,1,1] => 40040
[5,3,2,2,1,1,1,1,1] => 26604
[5,3,2,1,1,1,1,1,1,1] => 10400
[5,3,1,1,1,1,1,1,1,1,1] => 1932
[5,2,2,2,2,2,2] => 4480
[5,2,2,2,2,2,1,1] => 9940
[5,2,2,2,2,1,1,1,1] => 9730
[5,2,2,2,1,1,1,1,1,1] => 5696
[5,2,2,1,1,1,1,1,1,1,1] => 2240
[5,2,1,1,1,1,1,1,1,1,1,1] => 497
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 68
[4,4,4,4,1] => 6076
[4,4,4,3,2] => 17160
[4,4,4,3,1,1] => 24024
[4,4,4,2,2,1] => 28600
[4,4,4,2,1,1,1] => 27944
[4,4,4,1,1,1,1,1] => 10192
[4,4,3,3,3] => 8440
[4,4,3,3,2,1] => 40040
[4,4,3,3,1,1,1] => 32256
[4,4,3,2,2,2] => 25130
[4,4,3,2,2,1,1] => 51312
[4,4,3,2,1,1,1,1] => 38248
[4,4,3,1,1,1,1,1,1] => 12600
[4,4,2,2,2,2,1] => 20104
[4,4,2,2,2,1,1,1] => 24960
[4,4,2,2,1,1,1,1,1] => 16520
[4,4,2,1,1,1,1,1,1,1] => 6160
[4,4,1,1,1,1,1,1,1,1,1] => 1160
[4,3,3,3,3,1] => 11440
[4,3,3,3,2,2] => 16016
[4,3,3,3,2,1,1] => 30888
[4,3,3,3,1,1,1,1] => 18200
[4,3,3,2,2,2,1] => 27006
[4,3,3,2,2,1,1,1] => 32760
[4,3,3,2,1,1,1,1,1] => 19992
[4,3,3,1,1,1,1,1,1,1] => 6048
[4,3,2,2,2,2,2] => 8008
[4,3,2,2,2,2,1,1] => 18200
[4,3,2,2,2,1,1,1,1] => 17160
[4,3,2,2,1,1,1,1,1,1] => 9800
[4,3,2,1,1,1,1,1,1,1,1] => 3432
[4,3,1,1,1,1,1,1,1,1,1,1] => 616
[4,2,2,2,2,2,2,1] => 3640
[4,2,2,2,2,2,1,1,1] => 4970
[4,2,2,2,2,1,1,1,1,1] => 3960
[4,2,2,2,1,1,1,1,1,1,1] => 2048
[4,2,2,1,1,1,1,1,1,1,1,1] => 728
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 147
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 16
[3,3,3,3,3,2] => 2644
[3,3,3,3,3,1,1] => 3864
[3,3,3,3,2,2,1] => 7220
[3,3,3,3,2,1,1,1] => 8008
[3,3,3,3,1,1,1,1,1] => 3948
[3,3,3,2,2,2,2] => 3470
[3,3,3,2,2,2,1,1] => 8064
[3,3,3,2,2,1,1,1,1] => 7168
[3,3,3,2,1,1,1,1,1,1] => 3836
[3,3,3,1,1,1,1,1,1,1,1] => 980
[3,3,2,2,2,2,2,1] => 3432
[3,3,2,2,2,2,1,1,1] => 4736
[3,3,2,2,2,1,1,1,1,1] => 3640
[3,3,2,2,1,1,1,1,1,1,1] => 1904
[3,3,2,1,1,1,1,1,1,1,1,1] => 600
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 128
[3,2,2,2,2,2,2,2] => 600
[3,2,2,2,2,2,2,1,1] => 1330
[3,2,2,2,2,2,1,1,1,1] => 1444
[3,2,2,2,2,1,1,1,1,1,1] => 952
[3,2,2,2,1,1,1,1,1,1,1,1] => 472
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 140
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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:
2,1 3,2 3,4 5,4,2 6,4,2,3 5,4,2,4,5,1,0,1 5,2,0,8,0,0,4,3,0,4,0,2,2 4,3,3,1,2,0,4,0,4,1,2,0,1,1,3,0,1,0,1,0,3,0,3,0,0,0,2,0,0,1,0,1,0,0,0,0,0,0,1
$F_{3} = 2 + q$
$F_{4} = 3 + 2\ q$
$F_{5} = 3 + 4\ q$
$F_{6} = 5 + 4\ q + 2\ q^{2}$
$F_{7} = 6 + 4\ q + 2\ q^{2} + 3\ q^{3}$
$F_{8} = 5 + 4\ q + 2\ q^{2} + 4\ q^{3} + 5\ q^{4} + q^{5} + q^{7}$
$F_{9} = 5 + 2\ q + 8\ q^{3} + 4\ q^{6} + 3\ q^{7} + 4\ q^{9} + 2\ q^{11} + 2\ q^{12}$
$F_{10} = 4 + 3\ q + 3\ q^{2} + q^{3} + 2\ q^{4} + 4\ q^{6} + 4\ q^{8} + q^{9} + 2\ q^{10} + q^{12} + q^{13} + 3\ q^{14} + q^{16} + q^{18} + 3\ q^{20} + 3\ q^{22} + 2\ q^{26} + q^{29} + q^{31} + q^{38}$
$F_{11} = 5 + q + q^{4} + 7\ q^{5} + 2\ q^{6} + 4\ q^{10} + 2\ q^{11} + q^{15} + q^{16} + 3\ q^{20} + q^{24} + q^{25} + q^{26} + q^{29} + 3\ q^{30} + q^{34} + 3\ q^{40} + q^{44} + 3\ q^{45} + 4\ q^{50} + q^{54} + q^{55} + 2\ q^{56} + 3\ q^{60} + q^{80} + 2\ q^{105}$
$F_{12} = 4 + q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 2\ q^{7} + q^{9} + q^{10} + 2\ q^{12} + 2\ q^{13} + 3\ q^{14} + q^{17} + 2\ q^{19} + q^{26} + q^{29} + 2\ q^{32} + q^{34} + q^{36} + 2\ q^{37} + 2\ q^{44} + q^{45} + q^{47} + q^{56} + 2\ q^{59} + q^{66} + q^{71} + 2\ q^{72} + q^{74} + q^{77} + q^{79} + q^{82} + q^{86} + 2\ q^{87} + q^{90} + q^{93} + q^{98} + q^{102} + q^{110} + q^{113} + 3\ q^{117} + q^{121} + q^{128} + q^{132} + q^{133} + q^{144} + 2\ q^{146} + q^{155} + q^{163} + q^{169} + q^{176} + q^{177} + q^{187} + 2\ q^{234} + q^{238} + q^{241} + q^{327}$
$F_{13} = 4 + 2\ q + 2\ q^{5} + 4\ q^{8} + 2\ q^{17} + 2\ q^{19} + 2\ q^{21} + 2\ q^{22} + q^{26} + 2\ q^{27} + 2\ q^{30} + 2\ q^{45} + 2\ q^{48} + 2\ q^{50} + 2\ q^{57} + 2\ q^{100} + 2\ q^{102} + 2\ q^{112} + 2\ q^{113} + 2\ q^{114} + 2\ q^{115} + 4\ q^{132} + 2\ q^{140} + 2\ q^{162} + 2\ q^{170} + 2\ q^{172} + 2\ q^{198} + 2\ q^{215} + 2\ q^{220} + 2\ q^{246} + 2\ q^{255} + 2\ q^{256} + 2\ q^{261} + 2\ q^{320} + 2\ q^{330} + q^{340} + 2\ q^{351} + 2\ q^{360} + 2\ q^{384} + 2\ q^{423} + 2\ q^{440} + 4\ q^{462} + 2\ q^{510} + 2\ q^{575} + q^{656} + 2\ q^{660} + 2\ q^{792} + 2\ q^{810}$
$F_{14} = 3 + 2\ q + q^{2} + q^{3} + q^{6} + 2\ q^{7} + q^{9} + q^{10} + q^{13} + q^{19} + 2\ q^{20} + q^{25} + 2\ q^{27} + q^{31} + q^{32} + q^{34} + q^{44} + 2\ q^{45} + q^{47} + q^{51} + q^{54} + q^{62} + q^{64} + q^{65} + q^{66} + q^{72} + q^{78} + 2\ q^{156} + 2\ q^{163} + 2\ q^{176} + q^{192} + q^{201} + q^{204} + q^{207} + q^{213} + q^{214} + q^{215} + q^{221} + q^{222} + q^{224} + q^{232} + q^{234} + q^{254} + q^{257} + q^{258} + q^{264} + q^{280} + q^{284} + q^{300} + q^{303} + q^{306} + q^{339} + q^{363} + q^{394} + q^{414} + q^{462} + q^{465} + q^{468} + q^{474} + q^{478} + q^{483} + q^{495} + q^{505} + q^{508} + q^{519} + q^{520} + q^{523} + q^{535} + q^{540} + q^{550} + 2\ q^{555} + q^{567} + 2\ q^{572} + q^{714} + 2\ q^{728} + q^{732} + q^{747} + q^{750} + q^{752} + q^{759} + q^{762} + q^{767} + q^{799} + 2\ q^{832} + q^{834} + 2\ q^{891} + q^{924} + q^{936} + q^{972} + q^{984} + q^{986} + q^{990} + q^{1034} + q^{1050} + q^{1210} + q^{1225} + q^{1270} + q^{1285} + 2\ q^{1307} + q^{1449} + q^{1501} + q^{1509} + q^{1569} + q^{1695} + q^{1704} + q^{1715} + 2\ q^{1716} + q^{1768} + q^{1770} + q^{1810} + q^{2139} + q^{2241} + q^{2253} + 2\ q^{2288} + q^{2433} + q^{2451} + q^{2505}$
$F_{15} = 5 + q + q^{6} + q^{7} + 4\ q^{12} + 3\ q^{23} + q^{24} + q^{37} + q^{44} + 3\ q^{47} + 2\ q^{55} + q^{60} + 2\ q^{67} + q^{74} + q^{82} + q^{83} + q^{84} + q^{90} + 2\ q^{105} + q^{114} + q^{118} + q^{150} + q^{168} + q^{185} + q^{230} + q^{237} + q^{238} + q^{254} + q^{260} + 2\ q^{303} + 2\ q^{315} + q^{361} + 2\ q^{370} + q^{376} + q^{384} + q^{396} + q^{397} + q^{421} + q^{466} + q^{468} + q^{486} + q^{491} + q^{636} + q^{651} + q^{682} + q^{706} + q^{752} + q^{769} + q^{783} + q^{790} + q^{802} + q^{816} + q^{817} + q^{851} + q^{852} + q^{864} + q^{874} + q^{888} + q^{890} + q^{894} + q^{911} + q^{934} + q^{978} + 2\ q^{999} + 2\ q^{1068} + q^{1084} + q^{1156} + 2\ q^{1170} + q^{1177} + q^{1210} + q^{1393} + 2\ q^{1400} + q^{1407} + 2\ q^{1438} + q^{1449} + 2\ q^{1485} + q^{1554} + 2\ q^{1667} + 2\ q^{1671} + q^{1680} + q^{1769} + q^{1785} + 2\ q^{1801} + q^{1804} + 2\ q^{1911} + 2\ q^{1966} + q^{1995} + q^{2100} + 2\ q^{2122} + q^{2301} + q^{2371} + q^{2483} + q^{2486} + q^{2518} + q^{2521} + q^{2651} + 2\ q^{2670} + q^{2756} + q^{2940} + 2\ q^{3034} + q^{3066} + q^{3165} + q^{3266} + q^{3270} + 2\ q^{3337} + 2\ q^{3338} + q^{3406} + 2\ q^{3604} + q^{3680} + 2\ q^{3738} + q^{3792} + q^{3990} + q^{4100} + q^{4117} + q^{4200} + q^{4222} + 2\ q^{4290} + q^{4310} + q^{4494} + q^{4515} + 2\ q^{5004} + q^{5202} + q^{5274} + q^{5344} + 2\ q^{5405} + q^{5821} + q^{5856} + q^{6090} + q^{6195} + q^{6998} + q^{7012} + 2\ q^{7371} + q^{7680} + q^{7764} + q^{8077} + q^{8140} + q^{9764}$
$F_{16} = 4 + q + q^{3} + q^{4} + q^{7} + q^{10} + q^{13} + q^{14} + q^{18} + 2\ q^{28} + q^{43} + q^{44} + q^{51} + q^{54} + 2\ q^{65} + q^{68} + q^{75} + q^{83} + q^{87} + q^{88} + q^{93} + q^{95} + q^{105} + q^{111} + q^{114} + 2\ q^{121} + q^{126} + q^{133} + q^{138} + q^{155} + q^{202} + q^{220} + 2\ q^{336} + 2\ q^{364} + q^{422} + q^{429} + q^{436} + q^{446} + q^{531} + q^{549} + q^{555} + q^{562} + q^{611} + q^{625} + q^{630} + q^{672} + q^{744} + q^{763} + q^{770} + q^{779} + 2\ q^{780} + q^{831} + 2\ q^{880} + q^{1050} + q^{1070} + q^{1078} + q^{1105} + 2\ q^{1144} + q^{1216} + q^{1251} + q^{1260} + q^{1294} + q^{1305} + q^{1309} + q^{1323} + q^{1432} + q^{1464} + q^{1670} + q^{1705} + q^{1898} + q^{1917} + q^{1933} + q^{1980} + q^{2009} + q^{2023} + 2\ q^{2184} + q^{2194} + q^{2222} + 2\ q^{2240} + 2\ q^{2245} + q^{2256} + q^{2291} + q^{2433} + q^{2503} + 2\ q^{2520} + q^{2576} + q^{2608} + q^{2625} + q^{2670} + 2\ q^{2860} + q^{2940} + q^{2982} + 2\ q^{3088} + 2\ q^{3300} + q^{3451} + q^{3493} + q^{3514} + q^{3526} + q^{3556} + q^{3561} + q^{3572} + q^{3590} + q^{3617} + 2\ q^{3640} + q^{3650} + q^{4418} + q^{4481} + q^{4694} + q^{4729} + q^{4774} + q^{4802} + 2\ q^{4870} + q^{5225} + q^{5253} + 2\ q^{5473} + q^{5485} + q^{5555} + q^{5573} + q^{5608} + q^{5616} + q^{5630} + q^{6076} + q^{6083} + q^{6143} + 3\ q^{6160} + q^{6195} + q^{6213} + q^{6348} + q^{6411} + q^{6561} + q^{6568} + 2\ q^{7122} + q^{7392} + q^{7434} + q^{7455} + q^{7497} + q^{7643} + q^{8288} + 2\ q^{8320} + q^{8344} + q^{8785} + q^{8820} + q^{8855} + q^{8890} + 2\ q^{9152} + 2\ q^{9267} + q^{9478} + q^{9506} + q^{9856} + q^{9912} + 2\ q^{9913} + 2\ q^{10560} + q^{10633} + q^{10703} + q^{11231} + q^{11259} + q^{11277} + q^{11340} + q^{12613} + q^{12688} + q^{12800} + q^{13071} + q^{13134} + q^{13275} + q^{13293} + q^{13363} + q^{13380} + q^{13832} + q^{13944} + q^{15162} + q^{15246} + q^{15583} + q^{15618} + 2\ q^{16016} + 2\ q^{16183} + 2\ q^{17160} + 2\ q^{17472} + 2\ q^{18200} + q^{18813} + q^{18883} + q^{19685} + q^{19706} + q^{19709} + q^{19744} + 2\ q^{20020} + q^{20286} + q^{20349} + 2\ q^{21060} + 2\ q^{21840} + q^{25655} + q^{25690} + q^{28846} + 2\ q^{36036}$
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons.
Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Code
def statistic(mu):
s = SymmetricFunctions(QQ).s()
return DihedralGroup(mu.size()).cycle_index().scalar(s(mu))
Created
Sep 27, 2020 at 00:55 by Martin Rubey
Updated
Sep 27, 2020 at 00:55 by Martin Rubey
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