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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001380
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of monomer-dimer tilings of a Ferrers diagram.
For a hook of length $n$, this is the $n$-th Fibonacci number.
-----------------------------------------------------------------------------
References: [1] Triangle read by rows: T(n,k) (1 <= k <= n) = number of monomer-dimer tilings of an n X k board. [[OEIS:A210662]]
-----------------------------------------------------------------------------
Code:
from sage.combinat.tiling import TilingSolver, Polyomino
def statistic(la):
shape = Polyomino(Partition(la).cells())
p = Polyomino([(0, 0)])
q = Polyomino([(0, 0), (0, 1)])
T = TilingSolver([p, q], box=shape, reusable=True)
return T.number_of_solutions()
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 2
[1,1] => 2
[3] => 3
[2,1] => 3
[1,1,1] => 3
[4] => 5
[3,1] => 5
[2,2] => 7
[2,1,1] => 5
[1,1,1,1] => 5
[5] => 8
[4,1] => 8
[3,2] => 10
[3,1,1] => 8
[2,2,1] => 10
[2,1,1,1] => 8
[1,1,1,1,1] => 8
[6] => 13
[5,1] => 13
[4,2] => 17
[4,1,1] => 13
[3,3] => 22
[3,2,1] => 14
[3,1,1,1] => 13
[2,2,2] => 22
[2,2,1,1] => 17
[2,1,1,1,1] => 13
[1,1,1,1,1,1] => 13
[7] => 21
[6,1] => 21
[5,2] => 27
[5,1,1] => 21
[4,3] => 32
[4,2,1] => 24
[4,1,1,1] => 21
[3,3,1] => 32
[3,2,2] => 32
[3,2,1,1] => 24
[3,1,1,1,1] => 21
[2,2,2,1] => 32
[2,2,1,1,1] => 27
[2,1,1,1,1,1] => 21
[1,1,1,1,1,1,1] => 21
[8] => 34
[7,1] => 34
[6,2] => 44
[6,1,1] => 34
[5,3] => 54
[5,2,1] => 38
[5,1,1,1] => 34
[4,4] => 71
[4,3,1] => 47
[4,2,2] => 54
[4,2,1,1] => 41
[4,1,1,1,1] => 34
[3,3,2] => 67
[3,3,1,1] => 54
[3,2,2,1] => 47
[3,2,1,1,1] => 38
[3,1,1,1,1,1] => 34
[2,2,2,2] => 71
[2,2,2,1,1] => 54
[2,2,1,1,1,1] => 44
[2,1,1,1,1,1,1] => 34
[1,1,1,1,1,1,1,1] => 34
[9] => 55
[8,1] => 55
[7,2] => 71
[7,1,1] => 55
[6,3] => 86
[6,2,1] => 62
[6,1,1,1] => 55
[5,4] => 103
[5,3,1] => 79
[5,2,2] => 86
[5,2,1,1] => 65
[5,1,1,1,1] => 55
[4,4,1] => 103
[4,3,2] => 97
[4,3,1,1] => 79
[4,2,2,1] => 79
[4,2,1,1,1] => 65
[4,1,1,1,1,1] => 55
[3,3,3] => 131
[3,3,2,1] => 97
[3,3,1,1,1] => 86
[3,2,2,2] => 103
[3,2,2,1,1] => 79
[3,2,1,1,1,1] => 62
[3,1,1,1,1,1,1] => 55
[2,2,2,2,1] => 103
[2,2,2,1,1,1] => 86
[2,2,1,1,1,1,1] => 71
[2,1,1,1,1,1,1,1] => 55
[1,1,1,1,1,1,1,1,1] => 55
[10] => 89
[9,1] => 89
[8,2] => 115
[8,1,1] => 89
[7,3] => 140
[7,2,1] => 100
[7,1,1,1] => 89
[6,4] => 174
[6,3,1] => 126
[6,2,2] => 140
[6,2,1,1] => 106
[6,1,1,1,1] => 89
[5,5] => 228
[5,4,1] => 149
[5,3,2] => 164
[5,3,1,1] => 133
[5,2,2,1] => 126
[5,2,1,1,1] => 103
[5,1,1,1,1,1] => 89
[4,4,2] => 218
[4,4,1,1] => 174
[4,3,3] => 198
[4,3,2,1] => 140
[4,3,1,1,1] => 126
[4,2,2,2] => 174
[4,2,2,1,1] => 133
[4,2,1,1,1,1] => 106
[4,1,1,1,1,1,1] => 89
[3,3,3,1] => 198
[3,3,2,2] => 218
[3,3,2,1,1] => 164
[3,3,1,1,1,1] => 140
[3,2,2,2,1] => 149
[3,2,2,1,1,1] => 126
[3,2,1,1,1,1,1] => 100
[3,1,1,1,1,1,1,1] => 89
[2,2,2,2,2] => 228
[2,2,2,2,1,1] => 174
[2,2,2,1,1,1,1] => 140
[2,2,1,1,1,1,1,1] => 115
[2,1,1,1,1,1,1,1,1] => 89
[1,1,1,1,1,1,1,1,1,1] => 89
[11] => 144
[10,1] => 144
[9,2] => 186
[9,1,1] => 144
[8,3] => 226
[8,2,1] => 162
[8,1,1,1] => 144
[7,4] => 277
[7,3,1] => 205
[7,2,2] => 226
[7,2,1,1] => 171
[7,1,1,1,1] => 144
[6,5] => 331
[6,4,1] => 252
[6,3,2] => 261
[6,3,1,1] => 212
[6,2,2,1] => 205
[6,2,1,1,1] => 168
[6,1,1,1,1,1] => 144
[5,5,1] => 331
[5,4,2] => 317
[5,4,1,1] => 252
[5,3,3] => 329
[5,3,2,1] => 237
[5,3,1,1,1] => 212
[5,2,2,2] => 277
[5,2,2,1,1] => 212
[5,2,1,1,1,1] => 168
[5,1,1,1,1,1,1] => 144
[4,4,3] => 407
[4,4,2,1] => 316
[4,4,1,1,1] => 277
[4,3,3,1] => 298
[4,3,2,2] => 316
[4,3,2,1,1] => 237
[4,3,1,1,1,1] => 205
[4,2,2,2,1] => 252
[4,2,2,1,1,1] => 212
[4,2,1,1,1,1,1] => 171
[4,1,1,1,1,1,1,1] => 144
[3,3,3,2] => 407
[3,3,3,1,1] => 329
[3,3,2,2,1] => 317
[3,3,2,1,1,1] => 261
[3,3,1,1,1,1,1] => 226
[3,2,2,2,2] => 331
[3,2,2,2,1,1] => 252
[3,2,2,1,1,1,1] => 205
[3,2,1,1,1,1,1,1] => 162
[3,1,1,1,1,1,1,1,1] => 144
[2,2,2,2,2,1] => 331
[2,2,2,2,1,1,1] => 277
[2,2,2,1,1,1,1,1] => 226
[2,2,1,1,1,1,1,1,1] => 186
[2,1,1,1,1,1,1,1,1,1] => 144
[1,1,1,1,1,1,1,1,1,1,1] => 144
[12] => 233
[11,1] => 233
[10,2] => 301
[10,1,1] => 233
[9,3] => 366
[9,2,1] => 262
[9,1,1,1] => 233
[8,4] => 451
[8,3,1] => 331
[8,2,2] => 366
[8,2,1,1] => 277
[8,1,1,1,1] => 233
[7,5] => 559
[7,4,1] => 401
[7,3,2] => 425
[7,3,1,1] => 345
[7,2,2,1] => 331
[7,2,1,1,1] => 271
[7,1,1,1,1,1] => 233
[6,6] => 733
[6,5,1] => 481
[6,4,2] => 535
[6,4,1,1] => 426
[6,3,3] => 527
[6,3,2,1] => 377
[6,3,1,1,1] => 338
[6,2,2,2] => 451
[6,2,2,1,1] => 345
[6,2,1,1,1,1] => 274
[6,1,1,1,1,1,1] => 233
[5,5,2] => 699
[5,5,1,1] => 559
[5,4,3] => 584
[5,4,2,1] => 460
[5,4,1,1,1] => 401
[5,3,3,1] => 496
[5,3,2,2] => 534
[5,3,2,1,1] => 401
[5,3,1,1,1,1] => 345
[5,2,2,2,1] => 401
[5,2,2,1,1,1] => 338
[5,2,1,1,1,1,1] => 271
[5,1,1,1,1,1,1,1] => 233
[4,4,4] => 823
[4,4,3,1] => 616
[4,4,2,2] => 708
[4,4,2,1,1] => 534
[4,4,1,1,1,1] => 451
[4,3,3,2] => 616
[4,3,3,1,1] => 496
[4,3,2,2,1] => 460
[4,3,2,1,1,1] => 377
[4,3,1,1,1,1,1] => 331
[4,2,2,2,2] => 559
[4,2,2,2,1,1] => 426
[4,2,2,1,1,1,1] => 345
[4,2,1,1,1,1,1,1] => 277
[4,1,1,1,1,1,1,1,1] => 233
[3,3,3,3] => 823
[3,3,3,2,1] => 584
[3,3,3,1,1,1] => 527
[3,3,2,2,2] => 699
[3,3,2,2,1,1] => 535
[3,3,2,1,1,1,1] => 425
[3,3,1,1,1,1,1,1] => 366
[3,2,2,2,2,1] => 481
[3,2,2,2,1,1,1] => 401
[3,2,2,1,1,1,1,1] => 331
[3,2,1,1,1,1,1,1,1] => 262
[3,1,1,1,1,1,1,1,1,1] => 233
[2,2,2,2,2,2] => 733
[2,2,2,2,2,1,1] => 559
[2,2,2,2,1,1,1,1] => 451
[2,2,2,1,1,1,1,1,1] => 366
[2,2,1,1,1,1,1,1,1,1] => 301
[2,1,1,1,1,1,1,1,1,1,1] => 233
[1,1,1,1,1,1,1,1,1,1,1,1] => 233
[13] => 377
[12,1] => 377
[11,2] => 487
[11,1,1] => 377
[10,3] => 592
[10,2,1] => 424
[10,1,1,1] => 377
[9,4] => 728
[9,3,1] => 536
[9,2,2] => 592
[9,2,1,1] => 448
[9,1,1,1,1] => 377
[8,5] => 890
[8,4,1] => 653
[8,3,2] => 686
[8,3,1,1] => 557
[8,2,2,1] => 536
[8,2,1,1,1] => 439
[8,1,1,1,1,1] => 377
[7,6] => 1064
[7,5,1] => 812
[7,4,2] => 852
[7,4,1,1] => 678
[7,3,3] => 856
[7,3,2,1] => 614
[7,3,1,1,1] => 550
[7,2,2,2] => 728
[7,2,2,1,1] => 557
[7,2,1,1,1,1] => 442
[7,1,1,1,1,1,1] => 377
[6,6,1] => 1064
[6,5,2] => 1014
[6,5,1,1] => 812
[6,4,3] => 991
[6,4,2,1] => 776
[6,4,1,1,1] => 678
[6,3,3,1] => 794
[6,3,2,2] => 850
[6,3,2,1,1] => 638
[6,3,1,1,1,1] => 550
[6,2,2,2,1] => 653
[6,2,2,1,1,1] => 550
[6,2,1,1,1,1,1] => 442
[6,1,1,1,1,1,1,1] => 377
[5,5,3] => 1320
[5,5,2,1] => 1013
[5,5,1,1,1] => 890
[5,4,4] => 1230
[5,4,3,1] => 885
[5,4,2,2] => 1029
[5,4,2,1,1] => 777
[5,4,1,1,1,1] => 653
[5,3,3,2] => 1023
[5,3,3,1,1] => 825
[5,3,2,2,1] => 777
[5,3,2,1,1,1] => 638
[5,3,1,1,1,1,1] => 557
[5,2,2,2,2] => 890
[5,2,2,2,1,1] => 678
[5,2,2,1,1,1,1] => 550
[5,2,1,1,1,1,1,1] => 439
[5,1,1,1,1,1,1,1,1] => 377
[4,4,4,1] => 1230
[4,4,3,2] => 1262
[4,4,3,1,1] => 1023
[4,4,2,2,1] => 1029
[4,4,2,1,1,1] => 850
[4,4,1,1,1,1,1] => 728
[4,3,3,3] => 1230
[4,3,3,2,1] => 885
[4,3,3,1,1,1] => 794
[4,3,2,2,2] => 1013
[4,3,2,2,1,1] => 776
[4,3,2,1,1,1,1] => 614
[4,3,1,1,1,1,1,1] => 536
[4,2,2,2,2,1] => 812
[4,2,2,2,1,1,1] => 678
[4,2,2,1,1,1,1,1] => 557
[4,2,1,1,1,1,1,1,1] => 448
[4,1,1,1,1,1,1,1,1,1] => 377
[3,3,3,3,1] => 1230
[3,3,3,2,2] => 1320
[3,3,3,2,1,1] => 991
[3,3,3,1,1,1,1] => 856
[3,3,2,2,2,1] => 1014
[3,3,2,2,1,1,1] => 852
[3,3,2,1,1,1,1,1] => 686
[3,3,1,1,1,1,1,1,1] => 592
[3,2,2,2,2,2] => 1064
[3,2,2,2,2,1,1] => 812
[3,2,2,2,1,1,1,1] => 653
[3,2,2,1,1,1,1,1,1] => 536
[3,2,1,1,1,1,1,1,1,1] => 424
[3,1,1,1,1,1,1,1,1,1,1] => 377
[2,2,2,2,2,2,1] => 1064
[2,2,2,2,2,1,1,1] => 890
[2,2,2,2,1,1,1,1,1] => 728
[2,2,2,1,1,1,1,1,1,1] => 592
[2,2,1,1,1,1,1,1,1,1,1] => 487
[2,1,1,1,1,1,1,1,1,1,1,1] => 377
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 377
[14] => 610
[13,1] => 610
[12,2] => 788
[12,1,1] => 610
[11,3] => 958
[11,2,1] => 686
[11,1,1,1] => 610
[10,4] => 1179
[10,3,1] => 867
[10,2,2] => 958
[10,2,1,1] => 725
[10,1,1,1,1] => 610
[9,5] => 1449
[9,4,1] => 1054
[9,3,2] => 1111
[9,3,1,1] => 902
[9,2,2,1] => 867
[9,2,1,1,1] => 710
[9,1,1,1,1,1] => 610
[8,6] => 1797
[8,5,1] => 1293
[8,4,2] => 1387
[8,4,1,1] => 1104
[8,3,3] => 1383
[8,3,2,1] => 991
[8,3,1,1,1] => 888
[8,2,2,2] => 1179
[8,2,2,1,1] => 902
[8,2,1,1,1,1] => 716
[8,1,1,1,1,1,1] => 610
[7,7] => 2356
[7,6,1] => 1544
[7,5,2] => 1713
[7,5,1,1] => 1371
[7,4,3] => 1575
[7,4,2,1] => 1236
[7,4,1,1,1] => 1079
[7,3,3,1] => 1290
[7,3,2,2] => 1384
[7,3,2,1,1] => 1039
[7,3,1,1,1,1] => 895
[7,2,2,2,1] => 1054
[7,2,2,1,1,1] => 888
[7,2,1,1,1,1,1] => 713
[7,1,1,1,1,1,1,1] => 610
[6,6,2] => 2248
[6,6,1,1] => 1797
[6,5,3] => 1925
[6,5,2,1] => 1469
[6,5,1,1,1] => 1293
[6,4,4] => 2053
[6,4,3,1] => 1501
[6,4,2,2] => 1737
[6,4,2,1,1] => 1311
[6,4,1,1,1,1] => 1104
[6,3,3,2] => 1639
[6,3,3,1,1] => 1321
[6,3,2,2,1] => 1237
[6,3,2,1,1,1] => 1015
[6,3,1,1,1,1,1] => 888
[6,2,2,2,2] => 1449
[6,2,2,2,1,1] => 1104
[6,2,2,1,1,1,1] => 895
[6,2,1,1,1,1,1,1] => 716
[6,1,1,1,1,1,1,1,1] => 610
[5,5,4] => 2546
[5,5,3,1] => 1997
[5,5,2,2] => 2271
[5,5,2,1,1] => 1712
[5,5,1,1,1,1] => 1449
[5,4,4,1] => 1841
[5,4,3,2] => 1810
[5,4,3,1,1] => 1469
[5,4,2,2,1] => 1495
[5,4,2,1,1,1] => 1237
[5,4,1,1,1,1,1] => 1054
[5,3,3,3] => 2053
[5,3,3,2,1] => 1469
[5,3,3,1,1,1] => 1321
[5,3,2,2,2] => 1712
[5,3,2,2,1,1] => 1311
[5,3,2,1,1,1,1] => 1039
[5,3,1,1,1,1,1,1] => 902
[5,2,2,2,2,1] => 1293
[5,2,2,2,1,1,1] => 1079
[5,2,2,1,1,1,1,1] => 888
[5,2,1,1,1,1,1,1,1] => 710
[5,1,1,1,1,1,1,1,1,1] => 610
[4,4,4,2] => 2586
[4,4,4,1,1] => 2053
[4,4,3,3] => 2586
[4,4,3,2,1] => 1810
[4,4,3,1,1,1] => 1639
[4,4,2,2,2] => 2271
[4,4,2,2,1,1] => 1737
[4,4,2,1,1,1,1] => 1384
[4,4,1,1,1,1,1,1] => 1179
[4,3,3,3,1] => 1841
[4,3,3,2,2] => 1997
[4,3,3,2,1,1] => 1501
[4,3,3,1,1,1,1] => 1290
[4,3,2,2,2,1] => 1469
[4,3,2,2,1,1,1] => 1236
[4,3,2,1,1,1,1,1] => 991
[4,3,1,1,1,1,1,1,1] => 867
[4,2,2,2,2,2] => 1797
[4,2,2,2,2,1,1] => 1371
[4,2,2,2,1,1,1,1] => 1104
[4,2,2,1,1,1,1,1,1] => 902
[4,2,1,1,1,1,1,1,1,1] => 725
[4,1,1,1,1,1,1,1,1,1,1] => 610
[3,3,3,3,2] => 2546
[3,3,3,3,1,1] => 2053
[3,3,3,2,2,1] => 1925
[3,3,3,2,1,1,1] => 1575
[3,3,3,1,1,1,1,1] => 1383
[3,3,2,2,2,2] => 2248
[3,3,2,2,2,1,1] => 1713
[3,3,2,2,1,1,1,1] => 1387
[3,3,2,1,1,1,1,1,1] => 1111
[3,3,1,1,1,1,1,1,1,1] => 958
[3,2,2,2,2,2,1] => 1544
[3,2,2,2,2,1,1,1] => 1293
[3,2,2,2,1,1,1,1,1] => 1054
[3,2,2,1,1,1,1,1,1,1] => 867
[3,2,1,1,1,1,1,1,1,1,1] => 686
[3,1,1,1,1,1,1,1,1,1,1,1] => 610
[2,2,2,2,2,2,2] => 2356
[2,2,2,2,2,2,1,1] => 1797
[2,2,2,2,2,1,1,1,1] => 1449
[2,2,2,2,1,1,1,1,1,1] => 1179
[2,2,2,1,1,1,1,1,1,1,1] => 958
[2,2,1,1,1,1,1,1,1,1,1,1] => 788
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 610
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 610
[15] => 987
[14,1] => 987
[13,2] => 1275
[13,1,1] => 987
[12,3] => 1550
[12,2,1] => 1110
[12,1,1,1] => 987
[11,4] => 1907
[11,3,1] => 1403
[11,2,2] => 1550
[11,2,1,1] => 1173
[11,1,1,1,1] => 987
[10,5] => 2339
[10,4,1] => 1707
[10,3,2] => 1797
[10,3,1,1] => 1459
[10,2,2,1] => 1403
[10,2,1,1,1] => 1149
[10,1,1,1,1,1] => 987
[9,6] => 2861
[9,5,1] => 2105
[9,4,2] => 2239
[9,4,1,1] => 1782
[9,3,3] => 2239
[9,3,2,1] => 1605
[9,3,1,1,1] => 1438
[9,2,2,2] => 1907
[9,2,2,1,1] => 1459
[9,2,1,1,1,1] => 1158
[9,1,1,1,1,1,1] => 987
[8,7] => 3420
[8,6,1] => 2608
[8,5,2] => 2727
[8,5,1,1] => 2183
[8,4,3] => 2566
[8,4,2,1] => 2012
[8,4,1,1,1] => 1757
[8,3,3,1] => 2084
[8,3,2,2] => 2234
[8,3,2,1,1] => 1677
[8,3,1,1,1,1] => 1445
[8,2,2,2,1] => 1707
[8,2,2,1,1,1] => 1438
[8,2,1,1,1,1,1] => 1155
[8,1,1,1,1,1,1,1] => 987
[7,7,1] => 3420
[7,6,2] => 3264
[7,6,1,1] => 2608
[7,5,3] => 3245
[7,5,2,1] => 2482
[7,5,1,1,1] => 2183
[7,4,4] => 3283
[7,4,3,1] => 2386
[7,4,2,2] => 2766
[7,4,2,1,1] => 2088
[7,4,1,1,1,1] => 1757
[7,3,3,2] => 2662
[7,3,3,1,1] => 2146
[7,3,2,2,1] => 2014
[7,3,2,1,1,1] => 1653
[7,3,1,1,1,1,1] => 1445
[7,2,2,2,2] => 2339
[7,2,2,2,1,1] => 1782
[7,2,2,1,1,1,1] => 1445
[7,2,1,1,1,1,1,1] => 1155
[7,1,1,1,1,1,1,1,1] => 987
[6,6,3] => 4236
[6,6,2,1] => 3258
[6,6,1,1,1] => 2861
[6,5,4] => 3664
[6,5,3,1] => 2911
[6,5,2,2] => 3295
[6,5,2,1,1] => 2483
[6,5,1,1,1,1] => 2105
[6,4,4,1] => 3071
[6,4,3,2] => 3072
[6,4,3,1,1] => 2492
[6,4,2,2,1] => 2524
[6,4,2,1,1,1] => 2087
[6,4,1,1,1,1,1] => 1782
[6,3,3,3] => 3283
[6,3,3,2,1] => 2354
[6,3,3,1,1,1] => 2115
[6,3,2,2,2] => 2725
[6,3,2,2,1,1] => 2087
[6,3,2,1,1,1,1] => 1653
[6,3,1,1,1,1,1,1] => 1438
[6,2,2,2,2,1] => 2105
[6,2,2,2,1,1,1] => 1757
[6,2,2,1,1,1,1,1] => 1445
[6,2,1,1,1,1,1,1,1] => 1158
[6,1,1,1,1,1,1,1,1,1] => 987
[5,5,5] => 5096
[5,5,4,1] => 3804
[5,5,3,2] => 4095
[5,5,3,1,1] => 3317
[5,5,2,2,1] => 3301
[5,5,2,1,1,1] => 2725
[5,5,1,1,1,1,1] => 2339
[5,4,4,2] => 3862
[5,4,4,1,1] => 3071
[5,4,3,3] => 3724
[5,4,3,2,1] => 2595
[5,4,3,1,1,1] => 2354
[5,4,2,2,2] => 3301
[5,4,2,2,1,1] => 2524
[5,4,2,1,1,1,1] => 2014
[5,4,1,1,1,1,1,1] => 1707
[5,3,3,3,1] => 3071
[5,3,3,2,2] => 3317
[5,3,3,2,1,1] => 2492
[5,3,3,1,1,1,1] => 2146
[5,3,2,2,2,1] => 2483
[5,3,2,2,1,1,1] => 2088
[5,3,2,1,1,1,1,1] => 1677
[5,3,1,1,1,1,1,1,1] => 1459
[5,2,2,2,2,2] => 2861
[5,2,2,2,2,1,1] => 2183
[5,2,2,2,1,1,1,1] => 1757
[5,2,2,1,1,1,1,1,1] => 1438
[5,2,1,1,1,1,1,1,1,1] => 1149
[5,1,1,1,1,1,1,1,1,1,1] => 987
[4,4,4,3] => 4840
[4,4,4,2,1] => 3724
[4,4,4,1,1,1] => 3283
[4,4,3,3,1] => 3862
[4,4,3,2,2] => 4095
[4,4,3,2,1,1] => 3072
[4,4,3,1,1,1,1] => 2662
[4,4,2,2,2,1] => 3295
[4,4,2,2,1,1,1] => 2766
[4,4,2,1,1,1,1,1] => 2234
[4,4,1,1,1,1,1,1,1] => 1907
[4,3,3,3,2] => 3804
[4,3,3,3,1,1] => 3071
[4,3,3,2,2,1] => 2911
[4,3,3,2,1,1,1] => 2386
[4,3,3,1,1,1,1,1] => 2084
[4,3,2,2,2,2] => 3258
[4,3,2,2,2,1,1] => 2482
[4,3,2,2,1,1,1,1] => 2012
[4,3,2,1,1,1,1,1,1] => 1605
[4,3,1,1,1,1,1,1,1,1] => 1403
[4,2,2,2,2,2,1] => 2608
[4,2,2,2,2,1,1,1] => 2183
[4,2,2,2,1,1,1,1,1] => 1782
[4,2,2,1,1,1,1,1,1,1] => 1459
[4,2,1,1,1,1,1,1,1,1,1] => 1173
[4,1,1,1,1,1,1,1,1,1,1,1] => 987
[3,3,3,3,3] => 5096
[3,3,3,3,2,1] => 3664
[3,3,3,3,1,1,1] => 3283
[3,3,3,2,2,2] => 4236
[3,3,3,2,2,1,1] => 3245
[3,3,3,2,1,1,1,1] => 2566
[3,3,3,1,1,1,1,1,1] => 2239
[3,3,2,2,2,2,1] => 3264
[3,3,2,2,2,1,1,1] => 2727
[3,3,2,2,1,1,1,1,1] => 2239
[3,3,2,1,1,1,1,1,1,1] => 1797
[3,3,1,1,1,1,1,1,1,1,1] => 1550
[3,2,2,2,2,2,2] => 3420
[3,2,2,2,2,2,1,1] => 2608
[3,2,2,2,2,1,1,1,1] => 2105
[3,2,2,2,1,1,1,1,1,1] => 1707
[3,2,2,1,1,1,1,1,1,1,1] => 1403
[3,2,1,1,1,1,1,1,1,1,1,1] => 1110
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 987
[2,2,2,2,2,2,2,1] => 3420
[2,2,2,2,2,2,1,1,1] => 2861
[2,2,2,2,2,1,1,1,1,1] => 2339
[2,2,2,2,1,1,1,1,1,1,1] => 1907
[2,2,2,1,1,1,1,1,1,1,1,1] => 1550
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 1275
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 987
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 987
[16] => 1597
[15,1] => 1597
[14,2] => 2063
[14,1,1] => 1597
[13,3] => 2508
[13,2,1] => 1796
[13,1,1,1] => 1597
[12,4] => 3086
[12,3,1] => 2270
[12,2,2] => 2508
[12,2,1,1] => 1898
[12,1,1,1,1] => 1597
[11,5] => 3788
[11,4,1] => 2761
[11,3,2] => 2908
[11,3,1,1] => 2361
[11,2,2,1] => 2270
[11,2,1,1,1] => 1859
[11,1,1,1,1,1] => 1597
[10,6] => 4658
[10,5,1] => 3398
[10,4,2] => 3626
[10,4,1,1] => 2886
[10,3,3] => 3622
[10,3,2,1] => 2596
[10,3,1,1,1] => 2326
[10,2,2,2] => 3086
[10,2,2,1,1] => 2361
[10,2,1,1,1,1] => 1874
[10,1,1,1,1,1,1] => 1597
[9,7] => 5776
[9,6,1] => 4152
[9,5,2] => 4440
[9,5,1,1] => 3554
[9,4,3] => 4141
[9,4,2,1] => 3248
[9,4,1,1,1] => 2836
[9,3,3,1] => 3374
[9,3,2,2] => 3618
[9,3,2,1,1] => 2716
[9,3,1,1,1,1] => 2340
[9,2,2,2,1] => 2761
[9,2,2,1,1,1] => 2326
[9,2,1,1,1,1,1] => 1868
[9,1,1,1,1,1,1,1] => 1597
[8,8] => 7573
[8,7,1] => 4965
[8,6,2] => 5512
[8,6,1,1] => 4405
[8,5,3] => 5170
[8,5,2,1] => 3951
[8,5,1,1,1] => 3476
[8,4,4] => 5336
[8,4,3,1] => 3887
[8,4,2,2] => 4503
[8,4,2,1,1] => 3399
[8,4,1,1,1,1] => 2861
[8,3,3,2] => 4301
[8,3,3,1,1] => 3467
[8,3,2,2,1] => 3251
[8,3,2,1,1,1] => 2668
[8,3,1,1,1,1,1] => 2333
[8,2,2,2,2] => 3788
[8,2,2,2,1,1] => 2886
[8,2,2,1,1,1,1] => 2340
[8,2,1,1,1,1,1,1] => 1871
[8,1,1,1,1,1,1,1,1] => 1597
[7,7,2] => 7225
[7,7,1,1] => 5776
[7,6,3] => 6140
[7,6,2,1] => 4731
[7,6,1,1,1] => 4152
[7,5,4] => 6210
[7,5,3,1] => 4908
[7,5,2,2] => 5566
[7,5,2,1,1] => 4195
[7,5,1,1,1,1] => 3554
[7,4,4,1] => 4912
[7,4,3,2] => 4882
[7,4,3,1,1] => 3961
[7,4,2,2,1] => 4019
[7,4,2,1,1,1] => 3324
[7,4,1,1,1,1,1] => 2836
[7,3,3,3] => 5336
[7,3,3,2,1] => 3823
[7,3,3,1,1,1] => 3436
[7,3,2,2,2] => 4437
[7,3,2,2,1,1] => 3398
[7,3,2,1,1,1,1] => 2692
[7,3,1,1,1,1,1,1] => 2340
[7,2,2,2,2,1] => 3398
[7,2,2,2,1,1,1] => 2836
[7,2,2,1,1,1,1,1] => 2333
[7,2,1,1,1,1,1,1,1] => 1868
[7,1,1,1,1,1,1,1,1,1] => 1597
[6,6,4] => 8263
[6,6,3,1] => 6409
[6,6,2,2] => 7303
[6,6,2,1,1] => 5506
[6,6,1,1,1,1] => 4658
[6,5,5] => 7642
[6,5,4,1] => 5472
[6,5,3,2] => 5973
[6,5,3,1,1] => 4836
[6,5,2,2,1] => 4790
[6,5,2,1,1,1] => 3952
[6,5,1,1,1,1,1] => 3398
[6,4,4,2] => 6448
[6,4,4,1,1] => 5124
[6,4,3,3] => 6310
[6,4,3,2,1] => 4405
[6,4,3,1,1,1] => 3993
[6,4,2,2,2] => 5572
[6,4,2,2,1,1] => 4261
[6,4,2,1,1,1,1] => 3398
[6,4,1,1,1,1,1,1] => 2886
[6,3,3,3,1] => 4912
[6,3,3,2,2] => 5314
[6,3,3,2,1,1] => 3993
[6,3,3,1,1,1,1] => 3436
[6,3,2,2,2,1] => 3952
[6,3,2,2,1,1,1] => 3324
[6,3,2,1,1,1,1,1] => 2668
[6,3,1,1,1,1,1,1,1] => 2326
[6,2,2,2,2,2] => 4658
[6,2,2,2,2,1,1] => 3554
[6,2,2,2,1,1,1,1] => 2861
[6,2,2,1,1,1,1,1,1] => 2340
[6,2,1,1,1,1,1,1,1,1] => 1874
[6,1,1,1,1,1,1,1,1,1,1] => 1597
[5,5,5,1] => 7642
[5,5,4,2] => 8005
[5,5,4,1,1] => 6350
[5,5,3,3] => 8363
[5,5,3,2,1] => 5874
[5,5,3,1,1,1] => 5314
[5,5,2,2,2] => 7284
[5,5,2,2,1,1] => 5572
[5,5,2,1,1,1,1] => 4437
[5,5,1,1,1,1,1,1] => 3788
[5,4,4,3] => 7266
[5,4,4,2,1] => 5559
[5,4,4,1,1,1] => 4912
[5,4,3,3,1] => 5559
[5,4,3,2,2] => 5874
[5,4,3,2,1,1] => 4405
[5,4,3,1,1,1,1] => 3823
[5,4,2,2,2,1] => 4790
[5,4,2,2,1,1,1] => 4019
[5,4,2,1,1,1,1,1] => 3251
[5,4,1,1,1,1,1,1,1] => 2761
[5,3,3,3,2] => 6350
[5,3,3,3,1,1] => 5124
[5,3,3,2,2,1] => 4836
[5,3,3,2,1,1,1] => 3961
[5,3,3,1,1,1,1,1] => 3467
[5,3,2,2,2,2] => 5506
[5,3,2,2,2,1,1] => 4195
[5,3,2,2,1,1,1,1] => 3399
[5,3,2,1,1,1,1,1,1] => 2716
[5,3,1,1,1,1,1,1,1,1] => 2361
[5,2,2,2,2,2,1] => 4152
[5,2,2,2,2,1,1,1] => 3476
[5,2,2,2,1,1,1,1,1] => 2836
[5,2,2,1,1,1,1,1,1,1] => 2326
[5,2,1,1,1,1,1,1,1,1,1] => 1859
[5,1,1,1,1,1,1,1,1,1,1,1] => 1597
[4,4,4,4] => 10012
[4,4,4,3,1] => 7266
[4,4,4,2,2] => 8363
[4,4,4,2,1,1] => 6310
[4,4,4,1,1,1,1] => 5336
[4,4,3,3,2] => 8005
[4,4,3,3,1,1] => 6448
[4,4,3,2,2,1] => 5973
[4,4,3,2,1,1,1] => 4882
[4,4,3,1,1,1,1,1] => 4301
[4,4,2,2,2,2] => 7303
[4,4,2,2,2,1,1] => 5566
[4,4,2,2,1,1,1,1] => 4503
[4,4,2,1,1,1,1,1,1] => 3618
[4,4,1,1,1,1,1,1,1,1] => 3086
[4,3,3,3,3] => 7642
[4,3,3,3,2,1] => 5472
[4,3,3,3,1,1,1] => 4912
[4,3,3,2,2,2] => 6409
[4,3,3,2,2,1,1] => 4908
[4,3,3,2,1,1,1,1] => 3887
[4,3,3,1,1,1,1,1,1] => 3374
[4,3,2,2,2,2,1] => 4731
[4,3,2,2,2,1,1,1] => 3951
[4,3,2,2,1,1,1,1,1] => 3248
[4,3,2,1,1,1,1,1,1,1] => 2596
[4,3,1,1,1,1,1,1,1,1,1] => 2270
[4,2,2,2,2,2,2] => 5776
[4,2,2,2,2,2,1,1] => 4405
[4,2,2,2,2,1,1,1,1] => 3554
[4,2,2,2,1,1,1,1,1,1] => 2886
[4,2,2,1,1,1,1,1,1,1,1] => 2361
[4,2,1,1,1,1,1,1,1,1,1,1] => 1898
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 1597
[3,3,3,3,3,1] => 7642
[3,3,3,3,2,2] => 8263
[3,3,3,3,2,1,1] => 6210
[3,3,3,3,1,1,1,1] => 5336
[3,3,3,2,2,2,1] => 6140
[3,3,3,2,2,1,1,1] => 5170
[3,3,3,2,1,1,1,1,1] => 4141
[3,3,3,1,1,1,1,1,1,1] => 3622
[3,3,2,2,2,2,2] => 7225
[3,3,2,2,2,2,1,1] => 5512
[3,3,2,2,2,1,1,1,1] => 4440
[3,3,2,2,1,1,1,1,1,1] => 3626
[3,3,2,1,1,1,1,1,1,1,1] => 2908
[3,3,1,1,1,1,1,1,1,1,1,1] => 2508
[3,2,2,2,2,2,2,1] => 4965
[3,2,2,2,2,2,1,1,1] => 4152
[3,2,2,2,2,1,1,1,1,1] => 3398
[3,2,2,2,1,1,1,1,1,1,1] => 2761
[3,2,2,1,1,1,1,1,1,1,1,1] => 2270
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 1796
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1597
[2,2,2,2,2,2,2,2] => 7573
[2,2,2,2,2,2,2,1,1] => 5776
[2,2,2,2,2,2,1,1,1,1] => 4658
[2,2,2,2,2,1,1,1,1,1,1] => 3788
[2,2,2,2,1,1,1,1,1,1,1,1] => 3086
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 2508
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 2063
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1597
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1597
[17] => 2584
[16,1] => 2584
[15,2] => 3338
[15,1,1] => 2584
[14,3] => 4058
[14,2,1] => 2906
[14,1,1,1] => 2584
[13,4] => 4993
[13,3,1] => 3673
[13,2,2] => 4058
[13,2,1,1] => 3071
[13,1,1,1,1] => 2584
[12,5] => 6127
[12,4,1] => 4468
[12,3,2] => 4705
[12,3,1,1] => 3820
[12,2,2,1] => 3673
[12,2,1,1,1] => 3008
[12,1,1,1,1,1] => 2584
[11,6] => 7519
[11,5,1] => 5503
[11,4,2] => 5865
[11,4,1,1] => 4668
[11,3,3] => 5861
[11,3,2,1] => 4201
[11,3,1,1,1] => 3764
[11,2,2,2] => 4993
[11,2,2,1,1] => 3820
[11,2,1,1,1,1] => 3032
[11,1,1,1,1,1,1] => 2584
[10,7] => 9196
[10,6,1] => 6760
[10,5,2] => 7167
[10,5,1,1] => 5737
[10,4,3] => 6707
[10,4,2,1] => 5260
[10,4,1,1,1] => 4593
[10,3,3,1] => 5458
[10,3,2,2] => 5852
[10,3,2,1,1] => 4393
[10,3,1,1,1,1] => 3785
[10,2,2,2,1] => 4468
[10,2,2,1,1,1] => 3764
[10,2,1,1,1,1,1] => 3023
[10,1,1,1,1,1,1,1] => 2584
[9,8] => 10993
[9,7,1] => 8385
[9,6,2] => 8776
[9,6,1,1] => 7013
[9,5,3] => 8415
[9,5,2,1] => 6433
[9,5,1,1,1] => 5659
[9,4,4] => 8619
[9,4,3,1] => 6273
[9,4,2,2] => 7269
[9,4,2,1,1] => 5487
[9,4,1,1,1,1] => 4618
[9,3,3,2] => 6963
[9,3,3,1,1] => 5613
[9,3,2,2,1] => 5265
[9,3,2,1,1,1] => 4321
[9,3,1,1,1,1,1] => 3778
[9,2,2,2,2] => 6127
[9,2,2,2,1,1] => 4668
[9,2,2,1,1,1,1] => 3785
[9,2,1,1,1,1,1,1] => 3026
[9,1,1,1,1,1,1,1,1] => 2584
[8,8,1] => 10993
[8,7,2] => 10487
[8,7,1,1] => 8385
[8,6,3] => 10376
[8,6,2,1] => 7989
[8,6,1,1,1] => 7013
[8,5,4] => 9874
[8,5,3,1] => 7819
[8,5,2,2] => 8861
[8,5,2,1,1] => 6678
[8,5,1,1,1,1] => 5659
[8,4,4,1] => 7983
[8,4,3,2] => 7954
[8,4,3,1,1] => 6453
[8,4,2,2,1] => 6543
[8,4,2,1,1,1] => 5411
[8,4,1,1,1,1,1] => 4618
[8,3,3,3] => 8619
[8,3,3,2,1] => 6177
[8,3,3,1,1,1] => 5551
[8,3,2,2,2] => 7162
[8,3,2,2,1,1] => 5485
[8,3,2,1,1,1,1] => 4345
[8,3,1,1,1,1,1,1] => 3778
[8,2,2,2,2,1] => 5503
[8,2,2,2,1,1,1] => 4593
[8,2,2,1,1,1,1,1] => 3778
[8,2,1,1,1,1,1,1,1] => 3026
[8,1,1,1,1,1,1,1,1,1] => 2584
[7,7,3] => 13621
[7,7,2,1] => 10471
[7,7,1,1,1] => 9196
[7,6,4] => 12039
[7,6,3,1] => 9291
[7,6,2,2] => 10603
[7,6,2,1,1] => 7995
[7,6,1,1,1,1] => 6760
[7,5,5] => 12738
[7,5,4,1] => 9276
[7,5,3,2] => 10068
[7,5,3,1,1] => 8153
[7,5,2,2,1] => 8091
[7,5,2,1,1,1] => 6677
[7,5,1,1,1,1,1] => 5737
[7,4,4,2] => 10310
[7,4,4,1,1] => 8195
[7,4,3,3] => 10034
[7,4,3,2,1] => 7000
[7,4,3,1,1,1] => 6347
[7,4,2,2,2] => 8873
[7,4,2,2,1,1] => 6785
[7,4,2,1,1,1,1] => 5412
[7,4,1,1,1,1,1,1] => 4593
[7,3,3,3,1] => 7983
[7,3,3,2,2] => 8631
[7,3,3,2,1,1] => 6485
[7,3,3,1,1,1,1] => 5582
[7,3,2,2,2,1] => 6435
[7,3,2,2,1,1,1] => 5412
[7,3,2,1,1,1,1,1] => 4345
[7,3,1,1,1,1,1,1,1] => 3785
[7,2,2,2,2,2] => 7519
[7,2,2,2,2,1,1] => 5737
[7,2,2,2,1,1,1,1] => 4618
[7,2,2,1,1,1,1,1,1] => 3778
[7,2,1,1,1,1,1,1,1,1] => 3023
[7,1,1,1,1,1,1,1,1,1,1] => 2584
[6,6,5] => 15782
[6,6,4,1] => 12347
[6,6,3,2] => 13140
[6,6,3,1,1] => 10645
[6,6,2,2,1] => 10615
[6,6,2,1,1,1] => 8764
[6,6,1,1,1,1,1] => 7519
[6,5,5,1] => 11454
[6,5,4,2] => 11523
[6,5,4,1,1] => 9136
[6,5,3,3] => 12179
[6,5,3,2,1] => 8569
[6,5,3,1,1,1] => 7747
[6,5,2,2,2] => 10568
[6,5,2,2,1,1] => 8085
[6,5,2,1,1,1,1] => 6435
[6,5,1,1,1,1,1,1] => 5503
[6,4,4,3] => 12106
[6,4,4,2,1] => 9283
[6,4,4,1,1,1] => 8195
[6,4,3,3,1] => 9421
[6,4,3,2,2] => 9969
[6,4,3,2,1,1] => 7477
[6,4,3,1,1,1,1] => 6485
[6,4,2,2,2,1] => 8085
[6,4,2,2,1,1,1] => 6785
[6,4,2,1,1,1,1,1] => 5485
[6,4,1,1,1,1,1,1,1] => 4668
[6,3,3,3,2] => 10154
[6,3,3,3,1,1] => 8195
[6,3,3,2,2,1] => 7747
[6,3,3,2,1,1,1] => 6347
[6,3,3,1,1,1,1,1] => 5551
[6,3,2,2,2,2] => 8764
[6,3,2,2,2,1,1] => 6677
[6,3,2,2,1,1,1,1] => 5411
[6,3,2,1,1,1,1,1,1] => 4321
[6,3,1,1,1,1,1,1,1,1] => 3764
[6,2,2,2,2,2,1] => 6760
[6,2,2,2,2,1,1,1] => 5659
[6,2,2,2,1,1,1,1,1] => 4618
[6,2,2,1,1,1,1,1,1,1] => 3785
[6,2,1,1,1,1,1,1,1,1,1] => 3032
[6,1,1,1,1,1,1,1,1,1,1,1] => 2584
[5,5,5,2] => 15962
[5,5,5,1,1] => 12738
[5,5,4,3] => 14930
[5,5,4,2,1] => 11529
[5,5,4,1,1,1] => 10154
[5,5,3,3,1] => 12492
[5,5,3,2,2] => 13286
[5,5,3,2,1,1] => 9969
[5,5,3,1,1,1,1] => 8631
[5,5,2,2,2,1] => 10568
[5,5,2,2,1,1,1] => 8873
[5,5,2,1,1,1,1,1] => 7162
[5,5,1,1,1,1,1,1,1] => 6127
[5,4,4,4] => 14852
[5,4,4,3,1] => 10902
[5,4,4,2,2] => 12492
[5,4,4,2,1,1] => 9421
[5,4,4,1,1,1,1] => 7983
[5,4,3,3,2] => 11529
[5,4,3,3,1,1] => 9283
[5,4,3,2,2,1] => 8569
[5,4,3,2,1,1,1] => 7000
[5,4,3,1,1,1,1,1] => 6177
[5,4,2,2,2,2] => 10615
[5,4,2,2,2,1,1] => 8091
[5,4,2,2,1,1,1,1] => 6543
[5,4,2,1,1,1,1,1,1] => 5265
[5,4,1,1,1,1,1,1,1,1] => 4468
[5,3,3,3,3] => 12738
[5,3,3,3,2,1] => 9136
[5,3,3,3,1,1,1] => 8195
[5,3,3,2,2,2] => 10645
[5,3,3,2,2,1,1] => 8153
[5,3,3,2,1,1,1,1] => 6453
[5,3,3,1,1,1,1,1,1] => 5613
[5,3,2,2,2,2,1] => 7995
[5,3,2,2,2,1,1,1] => 6678
[5,3,2,2,1,1,1,1,1] => 5487
[5,3,2,1,1,1,1,1,1,1] => 4393
[5,3,1,1,1,1,1,1,1,1,1] => 3820
[5,2,2,2,2,2,2] => 9196
[5,2,2,2,2,2,1,1] => 7013
[5,2,2,2,2,1,1,1,1] => 5659
[5,2,2,2,1,1,1,1,1,1] => 4593
[5,2,2,1,1,1,1,1,1,1,1] => 3764
[5,2,1,1,1,1,1,1,1,1,1,1] => 3008
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 2584
[4,4,4,4,1] => 14852
[4,4,4,3,2] => 14930
[4,4,4,3,1,1] => 12106
[4,4,4,2,2,1] => 12179
[4,4,4,2,1,1,1] => 10034
[4,4,4,1,1,1,1,1] => 8619
[4,4,3,3,3] => 15962
[4,4,3,3,2,1] => 11523
[4,4,3,3,1,1,1] => 10310
[4,4,3,2,2,2] => 13140
[4,4,3,2,2,1,1] => 10068
[4,4,3,2,1,1,1,1] => 7954
[4,4,3,1,1,1,1,1,1] => 6963
[4,4,2,2,2,2,1] => 10603
[4,4,2,2,2,1,1,1] => 8861
[4,4,2,2,1,1,1,1,1] => 7269
[4,4,2,1,1,1,1,1,1,1] => 5852
[4,4,1,1,1,1,1,1,1,1,1] => 4993
[4,3,3,3,3,1] => 11454
[4,3,3,3,2,2] => 12347
[4,3,3,3,2,1,1] => 9276
[4,3,3,3,1,1,1,1] => 7983
[4,3,3,2,2,2,1] => 9291
[4,3,3,2,2,1,1,1] => 7819
[4,3,3,2,1,1,1,1,1] => 6273
[4,3,3,1,1,1,1,1,1,1] => 5458
[4,3,2,2,2,2,2] => 10471
[4,3,2,2,2,2,1,1] => 7989
[4,3,2,2,2,1,1,1,1] => 6433
[4,3,2,2,1,1,1,1,1,1] => 5260
[4,3,2,1,1,1,1,1,1,1,1] => 4201
[4,3,1,1,1,1,1,1,1,1,1,1] => 3673
[4,2,2,2,2,2,2,1] => 8385
[4,2,2,2,2,2,1,1,1] => 7013
[4,2,2,2,2,1,1,1,1,1] => 5737
[4,2,2,2,1,1,1,1,1,1,1] => 4668
[4,2,2,1,1,1,1,1,1,1,1,1] => 3820
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 3071
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2584
[3,3,3,3,3,2] => 15782
[3,3,3,3,3,1,1] => 12738
[3,3,3,3,2,2,1] => 12039
[3,3,3,3,2,1,1,1] => 9874
[3,3,3,3,1,1,1,1,1] => 8619
[3,3,3,2,2,2,2] => 13621
[3,3,3,2,2,2,1,1] => 10376
[3,3,3,2,2,1,1,1,1] => 8415
[3,3,3,2,1,1,1,1,1,1] => 6707
[3,3,3,1,1,1,1,1,1,1,1] => 5861
[3,3,2,2,2,2,2,1] => 10487
[3,3,2,2,2,2,1,1,1] => 8776
[3,3,2,2,2,1,1,1,1,1] => 7167
[3,3,2,2,1,1,1,1,1,1,1] => 5865
[3,3,2,1,1,1,1,1,1,1,1,1] => 4705
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 4058
[3,2,2,2,2,2,2,2] => 10993
[3,2,2,2,2,2,2,1,1] => 8385
[3,2,2,2,2,2,1,1,1,1] => 6760
[3,2,2,2,2,1,1,1,1,1,1] => 5503
[3,2,2,2,1,1,1,1,1,1,1,1] => 4468
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 3673
-----------------------------------------------------------------------------
Created: Apr 06, 2019 at 20:28 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Apr 06, 2019 at 20:28 by Martin Rubey