*****************************************************************************
* 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: St001601
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(mu):
s = SymmetricFunctions(QQ).s()
A = CombinatorialSpecies()
X = species.SingletonSpecies()
E = species.SetSpecies()
A.define(X*E(A))
V = (X + species.CharacteristicSpecies(2)).cycle_index_series() - (X^2).cycle_index_series()
F = V(A.cycle_index_series())
return F.coefficient(mu.size()).scalar(s(mu))
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 1
[1,1] => 0
[3] => 1
[2,1] => 1
[1,1,1] => 0
[4] => 2
[3,1] => 2
[2,2] => 2
[2,1,1] => 1
[1,1,1,1] => 1
[5] => 3
[4,1] => 6
[3,2] => 6
[3,1,1] => 5
[2,2,1] => 5
[2,1,1,1] => 3
[1,1,1,1,1] => 1
[6] => 6
[5,1] => 14
[4,2] => 23
[4,1,1] => 18
[3,3] => 8
[3,2,1] => 28
[3,1,1,1] => 16
[2,2,2] => 10
[2,2,1,1] => 11
[2,1,1,1,1] => 7
[1,1,1,1,1,1] => 1
[7] => 11
[6,1] => 37
[5,2] => 68
[5,1,1] => 61
[4,3] => 59
[4,2,1] => 128
[4,1,1,1] => 64
[3,3,1] => 68
[3,2,2] => 69
[3,2,1,1] => 101
[3,1,1,1,1] => 41
[2,2,2,1] => 39
[2,2,1,1,1] => 33
[2,1,1,1,1,1] => 14
[1,1,1,1,1,1,1] => 2
[8] => 23
[7,1] => 92
[6,2] => 214
[6,1,1] => 191
[5,3] => 244
[5,2,1] => 507
[5,1,1,1] => 251
[4,4] => 125
[4,3,1] => 499
[4,2,2] => 393
[4,2,1,1] => 562
[4,1,1,1,1] => 204
[3,3,2] => 260
[3,3,1,1] => 342
[3,2,2,1] => 400
[3,2,1,1,1] => 337
[3,1,1,1,1,1] => 99
[2,2,2,2] => 81
[2,2,2,1,1] => 134
[2,2,1,1,1,1] => 95
[2,1,1,1,1,1,1] => 29
[1,1,1,1,1,1,1,1] => 5
[9] => 47
[8,1] => 239
[7,2] => 632
[7,1,1] => 590
[6,3] => 948
[6,2,1] => 1877
[6,1,1,1] => 906
[5,4] => 760
[5,3,1] => 2568
[5,2,2] => 1831
[5,2,1,1] => 2689
[5,1,1,1,1] => 913
[4,4,1] => 1273
[4,3,2] => 2346
[4,3,1,1] => 2848
[4,2,2,1] => 2738
[4,2,1,1,1] => 2220
[4,1,1,1,1,1] => 602
[3,3,3] => 533
[3,3,2,1] => 2022
[3,3,1,1,1] => 1358
[3,2,2,2] => 962
[3,2,2,1,1] => 1746
[3,2,1,1,1,1] => 1055
[3,1,1,1,1,1,1] => 254
[2,2,2,2,1] => 427
[2,2,2,1,1,1] => 454
[2,2,1,1,1,1,1] => 242
[2,1,1,1,1,1,1,1] => 66
[1,1,1,1,1,1,1,1,1] => 9
[10] => 106
[9,1] => 613
[8,2] => 1890
[8,1,1] => 1773
[7,3] => 3369
[7,2,1] => 6611
[7,1,1,1] => 3197
[6,4] => 3678
[6,3,1] => 11445
[6,2,2] => 7878
[6,2,1,1] => 11515
[6,1,1,1,1] => 3819
[5,5] => 1585
[5,4,1] => 9743
[5,3,2] => 14194
[5,3,1,1] => 17089
[5,2,2,1] => 15188
[5,2,1,1,1] => 12139
[5,1,1,1,1,1] => 3111
[4,4,2] => 7662
[4,4,1,1] => 8586
[4,3,3] => 6027
[4,3,2,1] => 20795
[4,3,1,1,1] => 13373
[4,2,2,2] => 7744
[4,2,2,1,1] => 13883
[4,2,1,1,1,1] => 8022
[4,1,1,1,1,1,1] => 1748
[3,3,3,1] => 5358
[3,3,2,2] => 6144
[3,3,2,1,1] => 10635
[3,3,1,1,1,1] => 4921
[3,2,2,2,1] => 6467
[3,2,2,1,1,1] => 6707
[3,2,1,1,1,1,1] => 3165
[3,1,1,1,1,1,1,1] => 661
[2,2,2,2,2] => 893
[2,2,2,2,1,1] => 1777
[2,2,2,1,1,1,1] => 1426
[2,2,1,1,1,1,1,1] => 608
[2,1,1,1,1,1,1,1,1] => 151
[1,1,1,1,1,1,1,1,1,1] => 15
[11] => 235
[10,1] => 1607
[9,2] => 5549
[9,1,1] => 5296
[8,3] => 11609
[8,2,1] => 22578
[8,1,1,1] => 10872
[7,4] => 15479
[7,3,1] => 46858
[7,2,2] => 31550
[7,2,1,1] => 46349
[7,1,1,1,1] => 15133
[6,5] => 11542
[6,4,1] => 54159
[6,3,2] => 72738
[6,3,1,1] => 86667
[6,2,2,1] => 74630
[6,2,1,1,1] => 59052
[6,1,1,1,1,1] => 14789
[5,5,1] => 24658
[5,4,2] => 68375
[5,4,1,1] => 76452
[5,3,3] => 43710
[5,3,2,1] => 144690
[5,3,1,1,1] => 91226
[5,2,2,2] => 49117
[5,2,2,1,1] => 88123
[5,2,1,1,1,1] => 49487
[5,1,1,1,1,1,1] => 10276
[4,4,3] => 29490
[4,4,2,1] => 79538
[4,4,1,1,1] => 46984
[4,3,3,1] => 68964
[4,3,2,2] => 74144
[4,3,2,1,1] => 125136
[4,3,1,1,1,1] => 55831
[4,2,2,2,1] => 59705
[4,2,2,1,1,1] => 60603
[4,2,1,1,1,1,1] => 27234
[4,1,1,1,1,1,1,1] => 5040
[3,3,3,2] => 24536
[3,3,3,1,1] => 33976
[3,3,2,2,1] => 49340
[3,3,2,1,1,1] => 47071
[3,3,1,1,1,1,1] => 17024
[3,2,2,2,2] => 15538
[3,2,2,2,1,1] => 31529
[3,2,2,1,1,1,1] => 23703
[3,2,1,1,1,1,1,1] => 9256
[3,1,1,1,1,1,1,1,1] => 1676
[2,2,2,2,2,1] => 5603
[2,2,2,2,1,1,1] => 6704
[2,2,2,1,1,1,1,1] => 4231
[2,2,1,1,1,1,1,1,1] => 1574
[2,1,1,1,1,1,1,1,1,1] => 339
[1,1,1,1,1,1,1,1,1,1,1] => 31
[12] => 551
[11,1] => 4215
[10,2] => 16333
[10,1,1] => 15653
[9,3] => 38760
[9,2,1] => 75299
[9,1,1,1] => 36324
[8,4] => 61078
[8,3,1] => 181510
[8,2,2] => 121045
[8,2,1,1] => 177720
[8,1,1,1,1] => 57664
[7,5] => 60528
[7,4,1] => 259916
[7,3,2] => 335978
[7,3,1,1] => 399120
[7,2,2,1] => 337430
[7,2,1,1,1] => 265715
[7,1,1,1,1,1] => 65482
[6,6] => 25999
[6,5,1] => 201119
[6,4,2] => 433048
[6,4,1,1] => 480151
[6,3,3] => 257482
[6,3,2,1] => 834809
[6,3,1,1,1] => 520462
[6,2,2,2] => 272121
[6,2,2,1,1] => 486103
[6,2,1,1,1,1] => 269257
[6,1,1,1,1,1,1] => 54344
[5,5,2] => 205666
[5,5,1,1] => 223531
[5,4,3] => 312423
[5,4,2,1] => 811585
[5,4,1,1,1] => 470441
[5,3,3,1] => 565195
[5,3,2,2] => 586695
[5,3,2,1,1] => 981832
[5,3,1,1,1,1] => 427461
[5,2,2,2,1] => 429247
[5,2,2,1,1,1] => 430765
[5,2,1,1,1,1,1] => 188078
[5,1,1,1,1,1,1,1] => 32984
[4,4,4] => 65040
[4,4,3,1] => 389911
[4,4,2,2] => 336572
[4,4,2,1,1] => 549036
[4,4,1,1,1,1] => 223716
[4,3,3,2] => 365920
[4,3,3,1,1] => 497011
[4,3,2,2,1] => 670493
[4,3,2,1,1,1] => 625746
[4,3,1,1,1,1,1] => 215923
[4,2,2,2,2] => 163218
[4,2,2,2,1,1] => 328141
[4,2,2,1,1,1,1] => 240349
[4,2,1,1,1,1,1,1] => 88915
[4,1,1,1,1,1,1,1,1] => 14312
[3,3,3,3] => 53573
[3,3,3,2,1] => 233983
[3,3,3,1,1,1] => 175088
[3,3,2,2,2] => 140185
[3,3,2,2,1,1] => 276521
[3,3,2,1,1,1,1] => 188815
[3,3,1,1,1,1,1,1] => 56399
[3,2,2,2,2,1] => 113315
[3,2,2,2,1,1,1] => 132924
[3,2,2,1,1,1,1,1] => 79407
[3,2,1,1,1,1,1,1,1] => 26580
[3,1,1,1,1,1,1,1,1,1] => 4220
[2,2,2,2,2,2] => 12089
[2,2,2,2,2,1,1] => 26257
[2,2,2,2,1,1,1,1] => 23377
[2,2,2,1,1,1,1,1,1] => 12293
[2,2,1,1,1,1,1,1,1,1] => 4067
[2,1,1,1,1,1,1,1,1,1,1] => 771
[1,1,1,1,1,1,1,1,1,1,1,1] => 70
[13] => 1301
[12,1] => 11185
[11,2] => 47762
[11,1,1] => 46127
[10,3] => 127255
[10,2,1] => 246847
[10,1,1,1] => 119139
[9,4] => 229346
[9,3,1] => 676065
[9,2,2] => 447909
[9,2,1,1] => 658670
[9,1,1,1,1] => 212846
[8,5] => 278385
[8,4,1] => 1144224
[8,3,2] => 1449587
[8,3,1,1] => 1717613
[8,2,2,1] => 1438069
[8,2,1,1,1] => 1128922
[8,1,1,1,1,1] => 275966
[7,6] => 197647
[7,5,1] => 1184407
[7,4,2] => 2327430
[7,4,1,1] => 2571305
[7,3,3] => 1340266
[7,3,2,1] => 4293285
[7,3,1,1,1] => 2659384
[7,2,2,2] => 1368076
[7,2,2,1,1] => 2440040
[7,2,1,1,1,1] => 1339583
[7,1,1,1,1,1,1] => 265971
[6,6,1] => 514929
[6,5,2] => 1895823
[6,5,1,1] => 2038062
[6,4,3] => 2258136
[6,4,2,1] => 5745658
[6,4,1,1,1] => 3292138
[6,3,3,1] => 3714528
[6,3,2,2] => 3788514
[6,3,2,1,1] => 6302616
[6,3,1,1,1,1] => 2706883
[6,2,2,2,1] => 2644314
[6,2,2,1,1,1] => 2633866
[6,2,1,1,1,1,1] => 1131174
[6,1,1,1,1,1,1,1] => 192015
[5,5,3] => 1165047
[5,5,2,1] => 2781537
[5,5,1,1,1] => 1550827
[5,4,4] => 847178
[5,4,3,1] => 4649710
[5,4,2,2] => 3872760
[5,4,2,1,1] => 6267317
[5,4,1,1,1,1] => 2489670
[5,3,3,2] => 3383227
[5,3,3,1,1] => 4546875
[5,3,2,2,1] => 5926203
[5,3,2,1,1,1] => 5461337
[5,3,1,1,1,1,1] => 1833859
[5,2,2,2,2] => 1311440
[5,2,2,2,1,1] => 2625716
[5,2,2,1,1,1,1] => 1892064
[5,2,1,1,1,1,1,1] => 679491
[5,1,1,1,1,1,1,1,1] => 103044
[4,4,4,1] => 1015200
[4,4,3,2] => 2431424
[4,4,3,1,1] => 3190347
[4,4,2,2,1] => 3451400
[4,4,2,1,1,1] => 3093559
[4,4,1,1,1,1,1] => 968315
[4,3,3,3] => 931564
[4,3,3,2,1] => 3914420
[4,3,3,1,1,1] => 2866762
[4,3,2,2,2] => 2151821
[4,3,2,2,1,1] => 4192622
[4,3,2,1,1,1,1] => 2793583
[4,3,1,1,1,1,1,1] => 790474
[4,2,2,2,2,1] => 1329714
[4,2,2,2,1,1,1] => 1538707
[4,2,2,1,1,1,1,1] => 893026
[4,2,1,1,1,1,1,1,1] => 282301
[4,1,1,1,1,1,1,1,1,1] => 40059
[3,3,3,3,1] => 634936
[3,3,3,2,2] => 825150
[3,3,3,2,1,1] => 1509028
[3,3,3,1,1,1,1] => 798548
[3,3,2,2,2,1] => 1164093
[3,3,2,2,1,1,1] => 1310668
[3,3,2,1,1,1,1,1] => 708557
[3,3,1,1,1,1,1,1,1] => 180181
[3,2,2,2,2,2] => 274385
[3,2,2,2,2,1,1] => 595449
[3,2,2,2,1,1,1,1] => 513440
[3,2,2,1,1,1,1,1,1] => 256637
[3,2,1,1,1,1,1,1,1,1] => 75247
[3,1,1,1,1,1,1,1,1,1,1] => 10720
[2,2,2,2,2,2,1] => 83445
[2,2,2,2,2,1,1,1] => 107780
[2,2,2,2,1,1,1,1,1] => 77168
[2,2,2,1,1,1,1,1,1,1] => 35257
[2,2,1,1,1,1,1,1,1,1,1] => 10355
[2,1,1,1,1,1,1,1,1,1,1,1] => 1791
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 146
[14] => 3159
[13,1] => 29814
[12,2] => 139710
[12,1,1] => 135333
[11,3] => 411329
[11,2,1] => 798361
[11,1,1,1] => 386003
[10,4] => 834073
[10,3,1] => 2445124
[10,2,2] => 1614790
[10,2,1,1] => 2375470
[10,1,1,1,1] => 766564
[9,5] => 1182024
[9,4,1] => 4750303
[9,3,2] => 5947912
[9,3,1,1] => 7040935
[9,2,2,1] => 5858532
[9,2,1,1,1] => 4592037
[9,1,1,1,1,1] => 1116516
[8,6] => 1106219
[8,5,1] => 6022661
[8,4,2] => 11331314
[8,4,1,1] => 12483286
[8,3,3] => 6412124
[8,3,2,1] => 20396952
[8,3,1,1,1] => 12584960
[8,2,2,2] => 6416907
[8,2,2,1,1] => 11426124
[8,2,1,1,1,1] => 6241351
[8,1,1,1,1,1,1] => 1226218
[7,7] => 457936
[7,6,1] => 4374163
[7,5,2] => 12418029
[7,5,1,1] => 13281640
[7,4,3] => 13577282
[7,4,2,1] => 34133364
[7,4,1,1,1] => 19422287
[7,3,3,1] => 21330042
[7,3,2,2] => 21524687
[7,3,2,1,1] => 35688931
[7,3,1,1,1,1] => 15194856
[7,2,2,2,1] => 14638770
[7,2,2,1,1,1] => 14514035
[7,2,1,1,1,1,1] => 6168557
[7,1,1,1,1,1,1,1] => 1027464
[6,6,2] => 5530832
[6,6,1,1] => 5843245
[6,5,3] => 12163740
[6,5,2,1] => 28422596
[6,5,1,1,1] => 15653424
[6,4,4] => 7092162
[6,4,3,1] => 37252488
[6,4,2,2] => 30468044
[6,4,2,1,1] => 49014602
[6,4,1,1,1,1] => 19193837
[6,3,3,2] => 24701603
[6,3,3,1,1] => 32992512
[6,3,2,2,1] => 42211567
[6,3,2,1,1,1] => 38594984
[6,3,1,1,1,1,1] => 12748964
[6,2,2,2,2] => 8923061
[6,2,2,2,1,1] => 17796795
[6,2,2,1,1,1,1] => 12700060
[6,2,1,1,1,1,1,1] => 4476366
[6,1,1,1,1,1,1,1,1] => 656250
[5,5,4] => 4588445
[5,5,3,1] => 19542901
[5,5,2,2] => 15100271
[5,5,2,1,1] => 24017630
[5,5,1,1,1,1] => 9123199
[5,4,4,1] => 14782560
[5,4,3,2] => 32473666
[5,4,3,1,1] => 42181786
[5,4,2,2,1] => 44070267
[5,4,2,1,1,1] => 38996187
[5,4,1,1,1,1,1] => 11875398
[5,3,3,3] => 9753966
[5,3,3,2,1] => 40072376
[5,3,3,1,1,1] => 28962339
[5,3,2,2,2] => 21126463
[5,3,2,2,1,1] => 40903394
[5,3,2,1,1,1,1] => 26835840
[5,3,1,1,1,1,1,1] => 7370764
[5,2,2,2,2,1] => 11800944
[5,2,2,2,1,1,1] => 13540486
[5,2,2,1,1,1,1,1] => 7718442
[5,2,1,1,1,1,1,1,1] => 2361918
[5,1,1,1,1,1,1,1,1,1] => 315505
[4,4,4,2] => 7793175
[4,4,4,1,1] => 9491104
[4,4,3,3] => 7590151
[4,4,3,2,1] => 29251957
[4,4,3,1,1,1] => 20563691
[4,4,2,2,2] => 12595562
[4,4,2,2,1,1] => 24093381
[4,4,2,1,1,1,1] => 15339558
[4,4,1,1,1,1,1,1] => 3918017
[4,3,3,3,1] => 12320468
[4,3,3,2,2] => 15468142
[4,3,3,2,1,1] => 27978148
[4,3,3,1,1,1,1] => 14433875
[4,3,2,2,2,1] => 19769841
[4,3,2,2,1,1,1] => 21953065
[4,3,2,1,1,1,1,1] => 11535134
[4,3,1,1,1,1,1,1,1] => 2774995
[4,2,2,2,2,2] => 3577614
[4,2,2,2,2,1,1] => 7711691
[4,2,2,2,1,1,1,1] => 6540544
[4,2,2,1,1,1,1,1,1] => 3167585
[4,2,1,1,1,1,1,1,1,1] => 875787
[4,1,1,1,1,1,1,1,1,1,1] => 111183
[3,3,3,3,2] => 3270068
[3,3,3,3,1,1] => 4792094
[3,3,3,2,2,1] => 7811825
[3,3,3,2,1,1,1] => 8062022
[3,3,3,1,1,1,1,1] => 3347835
[3,3,2,2,2,2] => 3202606
[3,3,2,2,2,1,1] => 6828959
[3,3,2,2,1,1,1,1] => 5616773
[3,3,2,1,1,1,1,1,1] => 2531358
[3,3,1,1,1,1,1,1,1,1] => 561436
[3,2,2,2,2,2,1] => 2113779
[3,2,2,2,2,1,1,1] => 2692747
[3,2,2,2,1,1,1,1,1] => 1869222
[3,2,2,1,1,1,1,1,1,1] => 806995
[3,2,1,1,1,1,1,1,1,1,1] => 210661
[3,1,1,1,1,1,1,1,1,1,1,1] => 27293
[2,2,2,2,2,2,2] => 184569
[2,2,2,2,2,2,1,1] => 421402
[2,2,2,2,2,1,1,1,1] => 407084
[2,2,2,2,1,1,1,1,1,1] => 246293
[2,2,2,1,1,1,1,1,1,1,1] => 99641
[2,2,1,1,1,1,1,1,1,1,1,1] => 26308
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 4188
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 300
[15] => 7741
[14,1] => 80070
[13,2] => 407698
[13,1,1] => 396448
[12,3] => 1315703
[12,2,1] => 2554893
[12,1,1,1] => 1236913
[11,4] => 2956396
[11,3,1] => 8644171
[11,2,2] => 5696472
[11,2,1,1] => 8387392
[11,1,1,1,1] => 2704881
[10,5] => 4765767
[10,4,1] => 18898275
[10,3,2] => 23496430
[10,3,1,1] => 27796776
[10,2,2,1] => 23043188
[10,2,1,1,1] => 18046722
[10,1,1,1,1,1] => 4375450
[9,6] => 5392927
[9,5,1] => 28039356
[9,4,2] => 51507870
[9,4,1,1] => 56657895
[9,3,3] => 28857733
[9,3,2,1] => 91394303
[9,3,1,1,1] => 56256222
[9,2,2,2] => 28522314
[9,2,2,1,1] => 50747610
[9,2,1,1,1,1] => 27630647
[9,1,1,1,1,1,1] => 5393227
[8,7] => 3680071
[8,6,1] => 26917155
[8,5,2] => 69413437
[8,5,1,1] => 73986562
[8,4,3] => 72869745
[8,4,2,1] => 181839300
[8,4,1,1,1] => 103012526
[8,3,3,1] => 111578789
[8,3,2,2] => 111876391
[8,3,2,1,1] => 185082139
[8,3,1,1,1,1] => 78373063
[8,2,2,2,1] => 74903454
[8,2,2,1,1,1] => 74041064
[8,2,1,1,1,1,1] => 31260453
[8,1,1,1,1,1,1,1] => 5142814
[7,7,1] => 11294912
[7,6,2] => 51958371
[7,6,1,1] => 54604967
[7,5,3] => 88580529
[7,5,2,1] => 204392586
[7,5,1,1,1] => 111725750
[7,4,4] => 47915810
[7,4,3,1] => 245684271
[7,4,2,2] => 198785889
[7,4,2,1,1] => 318622205
[7,4,1,1,1,1] => 123641239
[7,3,3,2] => 155726348
[7,3,3,1,1] => 207169573
[7,3,2,2,1] => 262181817
[7,3,2,1,1,1] => 238505861
[7,3,1,1,1,1,1] => 77966757
[7,2,2,2,2] => 54015530
[7,2,2,2,1,1] => 107478710
[7,2,2,1,1,1,1] => 76207822
[7,2,1,1,1,1,1,1] => 26544034
[7,1,1,1,1,1,1,1,1] => 3810493
[6,6,3] => 41028234
[6,6,2,1] => 92065636
[6,6,1,1,1] => 49615262
[6,5,4] => 55183425
[6,5,3,1] => 224716966
[6,5,2,2] => 170501667
[6,5,2,1,1] => 269450329
[6,5,1,1,1,1] => 100876191
[6,4,4,1] => 136272209
[6,4,3,2] => 287269475
[6,4,3,1,1] => 370779824
[6,4,2,2,1] => 380210238
[6,4,2,1,1,1] => 333700641
[6,4,1,1,1,1,1] => 99950143
[6,3,3,3] => 79099966
[6,3,3,2,1] => 320677950
[6,3,3,1,1,1] => 229865023
[6,3,2,2,2] => 165224961
[6,3,2,2,1,1] => 318534239
[6,3,2,1,1,1,1] => 206947961
[6,3,1,1,1,1,1,1] => 55798819
[6,2,2,2,2,1] => 87742672
[6,2,2,2,1,1,1] => 100108275
[6,2,2,1,1,1,1,1] => 56414780
[6,2,1,1,1,1,1,1,1] => 16914682
[6,1,1,1,1,1,1,1,1,1] => 2182517
[5,5,5] => 10601065
[5,5,4,1] => 89587506
[5,5,3,2] => 154208313
[5,5,3,1,1] => 196712043
[5,5,2,2,1] => 190608325
[5,5,2,1,1,1] => 164935873
[5,5,1,1,1,1,1] => 47852403
[5,4,4,2] => 126330433
[5,4,4,1,1] => 152289589
[5,4,3,3] => 114181001
[5,4,3,2,1] => 430122068
[5,4,3,1,1,1] => 298337516
[5,4,2,2,2] => 177593697
[5,4,2,2,1,1] => 337553477
[5,4,2,1,1,1,1] => 211567561
[5,4,1,1,1,1,1,1] => 52475177
[5,3,3,3,1] => 141891644
[5,3,3,2,2] => 174825952
[5,3,3,2,1,1] => 314064097
[5,3,3,1,1,1,1] => 159519654
[5,3,2,2,2,1] => 212768324
[5,3,2,2,1,1,1] => 234205673
[5,3,2,1,1,1,1,1] => 120914379
[5,3,1,1,1,1,1,1,1] => 28175865
[5,2,2,2,2,2] => 34855610
[5,2,2,2,2,1,1] => 74821871
[5,2,2,2,1,1,1,1] => 62774905
[5,2,2,1,1,1,1,1,1] => 29814119
[5,2,1,1,1,1,1,1,1,1] => 7962468
[5,1,1,1,1,1,1,1,1,1,1] => 951628
[4,4,4,3] => 35198460
[4,4,4,2,1] => 106265601
[4,4,4,1,1,1] => 68491590
[4,4,3,3,1] => 112129534
[4,4,3,2,2] => 130559765
[4,4,3,2,1,1] => 231781016
[4,4,3,1,1,1,1] => 114215789
[4,4,2,2,2,1] => 128209364
[4,4,2,2,1,1,1] => 139131020
[4,4,2,1,1,1,1,1] => 69579125
[4,4,1,1,1,1,1,1,1] => 15064100
[4,3,3,3,2] => 70627893
[4,3,3,3,1,1] => 102402926
[4,3,3,2,2,1] => 161118282
[4,3,3,2,1,1,1] => 163980256
[4,3,3,1,1,1,1,1] => 66176812
[4,3,2,2,2,2] => 60086428
[4,3,2,2,2,1,1] => 127172749
[4,3,2,2,1,1,1,1] => 102925509
[4,3,2,1,1,1,1,1,1] => 44966322
[4,3,1,1,1,1,1,1,1,1] => 9426544
[4,2,2,2,2,2,1] => 30212659
[4,2,2,2,2,1,1,1] => 38129306
[4,2,2,2,1,1,1,1,1] => 25978311
[4,2,2,1,1,1,1,1,1,1] => 10844369
[4,2,1,1,1,1,1,1,1,1,1] => 2665923
[4,1,1,1,1,1,1,1,1,1,1,1] => 306753
[3,3,3,3,3] => 7414892
[3,3,3,3,2,1] => 35931031
[3,3,3,3,1,1,1] => 29042641
[3,3,3,2,2,2] => 24889100
[3,3,3,2,2,1,1] => 51236200
[3,3,3,2,1,1,1,1] => 38336453
[3,3,3,1,1,1,1,1,1] => 13192815
[3,3,2,2,2,2,1] => 27351064
[3,3,2,2,2,1,1,1] => 34031545
[3,3,2,2,1,1,1,1,1] => 22457491
[3,3,2,1,1,1,1,1,1,1] => 8711094
[3,3,1,1,1,1,1,1,1,1,1] => 1717430
[3,2,2,2,2,2,2] => 5159133
[3,2,2,2,2,2,1,1] => 11722580
[3,2,2,2,2,1,1,1,1] => 11117466
[3,2,2,2,1,1,1,1,1,1] => 6518838
[3,2,2,1,1,1,1,1,1,1,1] => 2482586
[3,2,1,1,1,1,1,1,1,1,1,1] => 584612
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 69257
[2,2,2,2,2,2,2,1] => 1353999
[2,2,2,2,2,2,1,1,1] => 1848347
[2,2,2,2,2,1,1,1,1,1] => 1453938
[2,2,2,2,1,1,1,1,1,1,1] => 767356
[2,2,2,1,1,1,1,1,1,1,1,1] => 278235
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 67094
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 9814
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 656
[16] => 19320
[15,1] => 216061
[14,2] => 1189556
[14,1,1] => 1159212
[13,3] => 4170302
[13,2,1] => 8106024
[13,1,1,1] => 3930653
[12,4] => 10279211
[12,3,1] => 30006637
[12,2,2] => 19753383
[12,2,1,1] => 29101308
[12,1,1,1,1] => 9386848
[11,5] => 18494567
[11,4,1] => 72763530
[11,3,2] => 90067696
[11,3,1,1] => 106534892
[11,2,2,1] => 88102161
[11,2,1,1,1] => 68979403
[11,1,1,1,1,1] => 16696041
[10,6] => 24254752
[10,5,1] => 122892268
[10,4,2] => 222576144
[10,4,1,1] => 244580813
[10,3,3] => 123922040
[10,3,2,1] => 391409134
[10,3,1,1,1] => 240581264
[10,2,2,2] => 121536738
[10,2,2,1,1] => 216117727
[10,2,1,1,1,1] => 117448034
[10,1,1,1,1,1,1] => 22828368
[9,7] => 21612921
[9,6,1] => 143071036
[9,5,2] => 351971969
[9,5,1,1] => 374384801
[9,4,3] => 361380673
[9,4,2,1] => 897533570
[9,4,1,1,1] => 507024487
[9,3,3,1] => 544884995
[9,3,2,2] => 544062168
[9,3,2,1,1] => 898813513
[9,3,1,1,1,1] => 379253339
[9,2,2,2,1] => 360684237
[9,2,2,1,1,1] => 355844180
[9,2,1,1,1,1,1] => 149589792
[9,1,1,1,1,1,1,1] => 24415222
[8,8] => 8760510
[8,7,1] => 99161817
[8,6,2] => 349683333
[8,6,1,1] => 366150035
[8,5,3] => 543060772
[8,5,2,1] => 1243258539
[8,5,1,1,1] => 676319266
[8,4,4] => 283788924
[8,4,3,1] => 1433978152
[8,4,2,2] => 1152565449
[8,4,2,1,1] => 1842813616
[8,4,1,1,1,1] => 710938182
[8,3,3,2] => 886313140
[8,3,3,1,1] => 1176077415
[8,3,2,2,1] => 1478229853
[8,3,2,1,1,1] => 1340242556
[8,3,1,1,1,1,1] => 435137053
[8,2,2,2,2] => 299858019
[8,2,2,2,1,1] => 595626017
[8,2,2,1,1,1,1] => 420560681
[8,2,1,1,1,1,1,1] => 145331970
[8,1,1,1,1,1,1,1,1] => 20581713
[7,7,2] => 149000354
[7,7,1,1] => 155021322
[7,6,3] => 426457640
[7,6,2,1] => 944658923
[7,6,1,1,1] => 505112478
[7,5,4] => 449426320
[7,5,3,1] => 1785220866
[7,5,2,2] => 1339892977
[7,5,2,1,1] => 2109002231
[7,5,1,1,1,1] => 782220335
[7,4,4,1] => 1004153097
[7,4,3,2] => 2069287572
[7,4,1,1,1,1,1] => 697881369
[7,3,3,3] => 546604386
[7,3,3,1,1,1] => 1566479393
[7,3,2,2,2] => 1116517038
[7,3,2,2,1,1] => 2146510361
[7,3,2,1,1,1,1] => 1385529982
[7,3,1,1,1,1,1,1] => 369153518
[7,2,2,2,2,1] => 576035138
[7,2,2,2,1,1,1] => 654720539
[7,2,2,1,1,1,1,1] => 366146407
[7,2,1,1,1,1,1,1,1] => 108332350
[7,1,1,1,1,1,1,1,1,1] => 13672266
[6,6,4] => 225366548
[6,6,3,1] => 835940916
[6,6,2,2] => 612687004
[6,6,2,1,1] => 958032046
[6,6,1,1,1,1] => 349789026
[6,5,5] => 153916570
[6,5,4,1] => 1179672035
[6,5,3,2] => 1948060968
[6,5,2,1,1,1] => 2014370852
[6,5,1,1,1,1,1] => 574732589
[6,4,4,2] => 1278890315
[6,4,4,1,1] => 1531505356
[6,4,3,3] => 1116359947
[6,4,2,2,2] => 1673723802
[6,4,2,1,1,1,1] => 1965518039
[6,4,1,1,1,1,1,1] => 478641242
[6,3,3,3,1] => 1254009175
[6,3,3,2,2] => 1527880853
[6,3,3,1,1,1,1] => 1374058482
[6,3,2,2,2,1] => 1808418064
[6,3,2,2,1,1,1] => 1979080876
[6,3,2,1,1,1,1,1] => 1010139662
[6,3,1,1,1,1,1,1,1] => 230731399
[6,2,2,2,2,2] => 281954418
[6,2,2,2,2,1,1] => 603383342
[6,2,2,2,1,1,1,1] => 502639242
[6,2,2,1,1,1,1,1,1] => 235664326
[6,2,1,1,1,1,1,1,1,1] => 61587484
[6,1,1,1,1,1,1,1,1,1,1] => 7100626
[5,5,5,1] => 233332763
[5,5,4,2] => 859977297
[5,5,4,1,1] => 1017777520
[5,5,3,3] => 622912614
[5,5,3,1,1,1] => 1526128383
[5,5,2,2,2] => 851526044
[5,5,2,2,1,1] => 1600988128
[5,5,2,1,1,1,1] => 977894241
[5,5,1,1,1,1,1,1] => 230434513
[5,4,4,3] => 639212749
[5,4,4,2,1] => 1886154628
[5,4,4,1,1,1] => 1199214079
[5,4,3,3,1] => 1845546086
[5,4,3,2,2] => 2108505383
[5,4,3,1,1,1,1] => 1803211980
[5,4,2,2,2,1] => 1971400025
[5,4,2,2,1,1,1] => 2120466640
[5,4,2,1,1,1,1,1] => 1041970902
[5,4,1,1,1,1,1,1,1] => 218622088
[5,3,3,3,2] => 893062007
[5,3,3,3,1,1] => 1285815884
[5,3,3,2,2,1] => 1984752879
[5,3,3,2,1,1,1] => 2002006225
[5,3,3,1,1,1,1,1] => 793831168
[5,3,2,2,2,2] => 706369146
[5,3,2,2,2,1,1] => 1488090962
[5,3,2,2,1,1,1,1] => 1191638033
[5,3,2,1,1,1,1,1,1] => 510643725
[5,3,1,1,1,1,1,1,1,1] => 103529268
[5,2,2,2,2,2,1] => 319974361
[5,2,2,2,2,1,1,1] => 401299508
[5,2,2,2,1,1,1,1,1] => 270076686
[5,2,2,1,1,1,1,1,1,1] => 110382466
[5,2,1,1,1,1,1,1,1,1,1] => 26183791
[5,1,1,1,1,1,1,1,1,1,1,1] => 2833086
[4,4,4,4] => 81445300
[4,4,4,3,1] => 585387997
[4,4,4,2,2] => 546087301
[4,4,4,2,1,1] => 936289405
[4,4,4,1,1,1,1] => 419841696
[4,4,3,3,2] => 721688662
[4,4,3,3,1,1] => 1026869763
[4,4,3,2,2,1] => 1497731903
[4,4,3,2,1,1,1] => 1489328769
[4,4,3,1,1,1,1,1] => 571987523
[4,4,2,2,2,2] => 431877205
[4,4,2,2,2,1,1] => 903808625
[4,4,2,2,1,1,1,1] => 712422962
[4,4,2,1,1,1,1,1,1] => 295385210
[4,4,1,1,1,1,1,1,1,1] => 55606834
[4,3,3,3,3] => 179399116
[4,3,3,3,2,1] => 849299983
[4,3,3,3,1,1,1] => 676850152
[4,3,3,2,2,2] => 563878601
[4,3,3,2,2,1,1] => 1152437656
[4,3,3,2,1,1,1,1] => 848296301
[4,3,3,1,1,1,1,1,1] => 283118706
[4,3,2,2,2,2,1] => 559248591
[4,3,2,2,2,1,1,1] => 689357878
[4,3,2,2,1,1,1,1,1] => 446635966
[4,3,2,1,1,1,1,1,1,1] => 167672615
[4,3,1,1,1,1,1,1,1,1,1] => 31188450
[4,2,2,2,2,2,2] => 80571211
[4,2,2,2,2,2,1,1] => 182171741
[4,2,2,2,2,1,1,1,1] => 170827464
[4,2,2,2,1,1,1,1,1,1] => 98143133
[4,2,2,1,1,1,1,1,1,1,1] => 36089145
[4,2,1,1,1,1,1,1,1,1,1,1] => 7993619
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 841222
[3,3,3,3,3,1] => 99230354
[3,3,3,3,2,2] => 139104308
[3,3,3,3,2,1,1] => 265485566
[3,3,3,3,1,1,1,1] => 153619100
[3,3,3,2,2,2,1] => 236051103
[3,3,3,2,2,1,1,1] => 281524281
[3,3,3,2,1,1,1,1,1] => 168099023
[3,3,3,1,1,1,1,1,1,1] => 49599833
[3,3,2,2,2,2,2] => 73980205
[3,3,2,2,2,2,1,1] => 166204079
[3,3,2,2,2,1,1,1,1] => 153393653
[3,3,2,2,1,1,1,1,1,1] => 85276255
[3,3,2,1,1,1,1,1,1,1,1] => 29110772
[3,3,1,1,1,1,1,1,1,1,1,1] => 5170779
[3,2,2,2,2,2,2,1] => 41343680
[3,2,2,2,2,2,1,1,1] => 55892916
[3,2,2,2,2,1,1,1,1,1] => 43119039
[3,2,2,2,1,1,1,1,1,1,1] => 21998628
[3,2,2,1,1,1,1,1,1,1,1,1] => 7505705
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 1610944
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 175655
[2,2,2,2,2,2,2,2] => 3060361
[2,2,2,2,2,2,2,1,1] => 7227055
[2,2,2,2,2,2,1,1,1,1] => 7441539
[2,2,2,2,2,1,1,1,1,1,1] => 4991567
[2,2,2,2,1,1,1,1,1,1,1,1] => 2343001
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 770623
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 171123
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 23146
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1471
[17] => 48629
[16,1] => 586218
[15,2] => 3467846
[15,1,1] => 3386978
[14,3] => 13126250
[14,2,1] => 25537889
[14,1,1,1] => 12400394
[13,4] => 35177106
[13,3,1] => 102622508
[13,2,2] => 67513490
[13,2,1,1] => 99533040
[13,1,1,1,1] => 32120017
[12,5] => 69727852
[12,4,1] => 272979999
[12,3,2] => 336954281
[12,3,1,1] => 398560232
[12,2,2,1] => 329103147
[12,2,1,1,1] => 257673721
[12,1,1,1,1,1] => 62321874
[11,6] => 103235767
[11,5,1] => 515092460
[11,4,2] => 924654054
[11,4,1,1] => 1015507413
[11,3,3] => 512766320
[11,3,2,1] => 1616809363
[11,3,1,1,1] => 992962590
[11,2,2,2] => 500373716
[11,2,2,1,1] => 889548863
[11,2,1,1,1,1] => 482878706
[11,1,1,1,1,1,1] => 93612969
[10,7] => 110500170
[10,6,1] => 696068032
[10,5,2] => 1667733412
[10,5,1,1] => 1771514683
[10,4,3] => 1689724841
[10,3,1,1,1,1] => 1745693272
[10,2,2,2,1] => 1654822837
[10,2,2,1,1,1] => 1630588267
[10,2,1,1,1,1,1] => 683544712
[10,1,1,1,1,1,1,1] => 110973066
[9,8] => 73068408
[9,7,1] => 631641770
[9,6,2] => 2015253662
[9,6,1,1] => 2105203721
[9,4,4] => 1534046483
[9,2,2,2,2] => 1556251897
[9,2,1,1,1,1,1,1] => 747314440
[9,1,1,1,1,1,1,1,1] => 104875176
[8,8,1] => 258123997
[8,7,2] => 1424325811
[8,7,1,1] => 1475963640
[8,2,1,1,1,1,1,1,1] => 637179940
[8,1,1,1,1,1,1,1,1,1] => 79255235
[7,7,3] => 1366069857
[7,7,1,1,1] => 1561318157
[7,5,5] => 1427903524
[7,3,1,1,1,1,1,1,1] => 1641626269
[7,2,2,2,2,2] => 1998987727
[7,2,2,1,1,1,1,1,1] => 1644684843
[7,2,1,1,1,1,1,1,1,1] => 423661448
[7,1,1,1,1,1,1,1,1,1,1] => 47735271
[6,6,5] => 896802718
[6,3,1,1,1,1,1,1,1,1] => 911759914
[6,2,2,1,1,1,1,1,1,1] => 938149496
[6,2,1,1,1,1,1,1,1,1,1] => 217528903
[6,1,1,1,1,1,1,1,1,1,1,1] => 22680279
[5,5,1,1,1,1,1,1,1] => 1038508895
[5,4,4,4] => 1686828508
[5,4,1,1,1,1,1,1,1,1] => 869125100
[5,3,2,1,1,1,1,1,1,1] => 2050347301
[5,3,1,1,1,1,1,1,1,1,1] => 368394234
[5,2,2,2,2,2,2] => 924289738
[5,2,2,2,2,2,1,1] => 2082822046
[5,2,2,2,2,1,1,1,1] => 1938098151
[5,2,2,2,1,1,1,1,1,1] => 1098518103
[5,2,2,1,1,1,1,1,1,1,1] => 394998239
[5,2,1,1,1,1,1,1,1,1,1,1] => 84350298
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 8337993
[4,4,4,4,1] => 1554824404
[4,4,3,3,3] => 2095030234
[4,4,2,1,1,1,1,1,1,1] => 1191011518
[4,4,1,1,1,1,1,1,1,1,1] => 198577406
[4,3,3,1,1,1,1,1,1,1] => 1148155856
[4,3,2,2,2,2,2] => 1645211384
[4,3,2,2,1,1,1,1,1,1] => 1828949030
[4,3,2,1,1,1,1,1,1,1,1] => 603460141
[4,3,1,1,1,1,1,1,1,1,1,1] => 100977256
[4,2,2,2,2,2,2,1] => 698477783
[4,2,2,2,2,2,1,1,1] => 937974055
[4,2,2,2,2,1,1,1,1,1] => 714403678
[4,2,2,2,1,1,1,1,1,1,1] => 356629696
[4,2,2,1,1,1,1,1,1,1,1,1] => 117363525
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 23672689
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2294544
[3,3,3,3,3,2] => 550627427
[3,3,3,3,3,1,1] => 841820636
[3,3,3,3,2,2,1] => 1477381616
[3,3,3,3,2,1,1,1] => 1613487021
[3,3,3,3,1,1,1,1,1] => 739238529
[3,3,3,2,2,2,2] => 713723839
[3,3,3,2,2,2,1,1] => 1572682059
[3,3,3,2,2,1,1,1,1] => 1384478476
[3,3,3,2,1,1,1,1,1,1] => 693840450
[3,3,3,1,1,1,1,1,1,1,1] => 179680925
[3,3,2,2,2,2,2,1] => 646164810
[3,3,2,2,2,2,1,1,1] => 860698503
[3,3,2,2,2,1,1,1,1,1] => 644565043
[3,3,2,2,1,1,1,1,1,1,1] => 311101182
[3,3,2,1,1,1,1,1,1,1,1,1] => 94999028
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 15357703
[3,2,2,2,2,2,2,2] => 101626430
[3,2,2,2,2,2,2,1,1] => 238883406
[3,2,2,2,2,2,1,1,1,1] => 243031850
[3,2,2,2,2,1,1,1,1,1,1] => 159683816
[3,2,2,2,1,1,1,1,1,1,1,1] => 72322221
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 22375667
-----------------------------------------------------------------------------
Created: Sep 27, 2020 at 00:18 by Martin Rubey
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Last Updated: Sep 27, 2020 at 00:18 by Martin Rubey