***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * 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: 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