***************************************************************************** * 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: St001606 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(mu): s = SymmetricFunctions(QQ).s() F = species.PartitionSpecies().cycle_index_series() return F.coefficient(mu.size()).scalar(s(mu)) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 2 [1,1] => 0 [3] => 3 [2,1] => 1 [1,1,1] => 0 [4] => 5 [3,1] => 2 [2,2] => 2 [2,1,1] => 0 [1,1,1,1] => 0 [5] => 7 [4,1] => 5 [3,2] => 4 [3,1,1] => 0 [2,2,1] => 1 [2,1,1,1] => 0 [1,1,1,1,1] => 0 [6] => 11 [5,1] => 8 [4,2] => 10 [4,1,1] => 1 [3,3] => 2 [3,2,1] => 2 [3,1,1,1] => 0 [2,2,2] => 2 [2,2,1,1] => 0 [2,1,1,1,1] => 0 [1,1,1,1,1,1] => 0 [7] => 15 [6,1] => 15 [5,2] => 17 [5,1,1] => 2 [4,3] => 10 [4,2,1] => 7 [4,1,1,1] => 0 [3,3,1] => 1 [3,2,2] => 4 [3,2,1,1] => 0 [3,1,1,1,1] => 0 [2,2,2,1] => 1 [2,2,1,1,1] => 0 [2,1,1,1,1,1] => 0 [1,1,1,1,1,1,1] => 0 [8] => 22 [7,1] => 23 [6,2] => 32 [6,1,1] => 5 [5,3] => 20 [5,2,1] => 14 [5,1,1,1] => 0 [4,4] => 12 [4,3,1] => 9 [4,2,2] => 11 [4,2,1,1] => 1 [4,1,1,1,1] => 0 [3,3,2] => 2 [3,3,1,1] => 0 [3,2,2,1] => 2 [3,2,1,1,1] => 0 [3,1,1,1,1,1] => 0 [2,2,2,2] => 2 [2,2,2,1,1] => 0 [2,2,1,1,1,1] => 0 [2,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1] => 0 [9] => 30 [8,1] => 37 [7,2] => 51 [7,1,1] => 10 [6,3] => 44 [6,2,1] => 29 [6,1,1,1] => 0 [5,4] => 27 [5,3,1] => 22 [5,2,2] => 22 [5,2,1,1] => 3 [5,1,1,1,1] => 0 [4,4,1] => 15 [4,3,2] => 14 [4,3,1,1] => 2 [4,2,2,1] => 7 [4,2,1,1,1] => 0 [4,1,1,1,1,1] => 0 [3,3,3] => 0 [3,3,2,1] => 1 [3,3,1,1,1] => 0 [3,2,2,2] => 4 [3,2,2,1,1] => 0 [3,2,1,1,1,1] => 0 [3,1,1,1,1,1,1] => 0 [2,2,2,2,1] => 1 [2,2,2,1,1,1] => 0 [2,2,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1] => 0 [10] => 42 [9,1] => 55 [8,2] => 84 [8,1,1] => 18 [7,3] => 76 [7,2,1] => 53 [7,1,1,1] => 1 [6,4] => 66 [6,3,1] => 53 [6,2,2] => 44 [6,2,1,1] => 7 [6,1,1,1,1] => 0 [5,5] => 16 [5,4,1] => 39 [5,3,2] => 36 [5,3,1,1] => 8 [5,2,2,1] => 16 [5,2,1,1,1] => 0 [5,1,1,1,1,1] => 0 [4,4,2] => 25 [4,4,1,1] => 5 [4,3,3] => 5 [4,3,2,1] => 10 [4,3,1,1,1] => 0 [4,2,2,2] => 11 [4,2,2,1,1] => 1 [4,2,1,1,1,1] => 0 [4,1,1,1,1,1,1] => 0 [3,3,3,1] => 0 [3,3,2,2] => 2 [3,3,2,1,1] => 0 [3,3,1,1,1,1] => 0 [3,2,2,2,1] => 2 [3,2,2,1,1,1] => 0 [3,2,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1] => 0 [2,2,2,2,2] => 2 [2,2,2,2,1,1] => 0 [2,2,2,1,1,1,1] => 0 [2,2,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1] => 0 [11] => 56 [10,1] => 83 [9,2] => 128 [9,1,1] => 31 [8,3] => 134 [8,2,1] => 94 [8,1,1,1] => 2 [7,4] => 121 [7,3,1] => 105 [7,2,2] => 78 [7,2,1,1] => 17 [7,1,1,1,1] => 0 [6,5] => 67 [6,4,1] => 101 [6,3,2] => 88 [6,3,1,1] => 20 [6,2,2,1] => 35 [6,2,1,1,1] => 0 [6,1,1,1,1,1] => 0 [5,5,1] => 28 [5,4,2] => 70 [5,4,1,1] => 19 [5,3,3] => 17 [5,3,2,1] => 32 [5,3,1,1,1] => 1 [5,2,2,2] => 23 [5,2,2,1,1] => 3 [5,2,1,1,1,1] => 0 [5,1,1,1,1,1,1] => 0 [4,4,3] => 22 [4,4,2,1] => 21 [4,4,1,1,1] => 0 [4,3,3,1] => 4 [4,3,2,2] => 14 [4,3,2,1,1] => 2 [4,3,1,1,1,1] => 0 [4,2,2,2,1] => 7 [4,2,2,1,1,1] => 0 [4,2,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1] => 0 [3,3,3,2] => 0 [3,3,3,1,1] => 0 [3,3,2,2,1] => 1 [3,3,2,1,1,1] => 0 [3,3,1,1,1,1,1] => 0 [3,2,2,2,2] => 4 [3,2,2,2,1,1] => 0 [3,2,2,1,1,1,1] => 0 [3,2,1,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,1] => 1 [2,2,2,2,1,1,1] => 0 [2,2,2,1,1,1,1,1] => 0 [2,2,1,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1,1] => 0 [12] => 77 [11,1] => 118 [10,2] => 197 [10,1,1] => 52 [9,3] => 216 [9,2,1] => 156 [9,1,1,1] => 5 [8,4] => 223 [8,3,1] => 198 [8,2,2] => 139 [8,2,1,1] => 34 [8,1,1,1,1] => 0 [7,5] => 144 [7,4,1] => 208 [7,3,2] => 176 [7,3,1,1] => 50 [7,2,2,1] => 68 [7,2,1,1,1] => 1 [7,1,1,1,1,1] => 0 [6,6] => 68 [6,5,1] => 118 [6,4,2] => 186 [6,4,1,1] => 51 [6,3,3] => 52 [6,3,2,1] => 83 [6,3,1,1,1] => 2 [6,2,2,2] => 49 [6,2,2,1,1] => 8 [6,2,1,1,1,1] => 0 [6,1,1,1,1,1,1] => 0 [5,5,2] => 55 [5,5,1,1] => 20 [5,4,3] => 66 [5,4,2,1] => 73 [5,4,1,1,1] => 3 [5,3,3,1] => 20 [5,3,2,2] => 40 [5,3,2,1,1] => 10 [5,3,1,1,1,1] => 0 [5,2,2,2,1] => 16 [5,2,2,1,1,1] => 0 [5,2,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1] => 0 [4,4,4] => 24 [4,4,3,1] => 22 [4,4,2,2] => 27 [4,4,2,1,1] => 5 [4,4,1,1,1,1] => 0 [4,3,3,2] => 5 [4,3,3,1,1] => 1 [4,3,2,2,1] => 10 [4,3,2,1,1,1] => 0 [4,3,1,1,1,1,1] => 0 [4,2,2,2,2] => 11 [4,2,2,2,1,1] => 1 [4,2,2,1,1,1,1] => 0 [4,2,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1] => 0 [3,3,3,3] => 0 [3,3,3,2,1] => 0 [3,3,3,1,1,1] => 0 [3,3,2,2,2] => 2 [3,3,2,2,1,1] => 0 [3,3,2,1,1,1,1] => 0 [3,3,1,1,1,1,1,1] => 0 [3,2,2,2,2,1] => 2 [3,2,2,2,1,1,1] => 0 [3,2,2,1,1,1,1,1] => 0 [3,2,1,1,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2] => 2 [2,2,2,2,2,1,1] => 0 [2,2,2,2,1,1,1,1] => 0 [2,2,2,1,1,1,1,1,1] => 0 [2,2,1,1,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1,1,1] => 0 [13] => 101 [12,1] => 171 [11,2] => 288 [11,1,1] => 82 [10,3] => 347 [10,2,1] => 256 [10,1,1,1] => 10 [9,4] => 372 [9,3,1] => 347 [9,2,2] => 229 [9,2,1,1] => 65 [9,1,1,1,1] => 0 [8,5] => 297 [8,4,1] => 406 [8,3,2] => 341 [8,3,1,1] => 103 [8,2,2,1] => 130 [8,2,1,1,1] => 3 [8,1,1,1,1,1] => 0 [7,6] => 176 [7,5,1] => 287 [7,4,2] => 391 [7,4,1,1] => 126 [7,3,3] => 119 [7,3,2,1] => 185 [7,3,1,1,1] => 8 [7,2,2,2] => 90 [7,2,2,1,1] => 19 [7,2,1,1,1,1] => 0 [7,1,1,1,1,1,1] => 0 [6,6,1] => 127 [6,5,2] => 234 [6,5,1,1] => 75 [6,4,3] => 194 [6,4,2,1] => 204 [6,4,1,1,1] => 8 [6,3,3,1] => 62 [6,3,2,2] => 106 [6,3,2,1,1] => 28 [6,3,1,1,1,1] => 0 [6,2,2,2,1] => 37 [6,2,2,1,1,1] => 0 [6,2,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1] => 0 [5,5,3] => 59 [5,5,2,1] => 73 [5,5,1,1,1] => 7 [5,4,4] => 68 [5,4,3,1] => 88 [5,4,2,2] => 89 [5,4,2,1,1] => 27 [5,4,1,1,1,1] => 0 [5,3,3,2] => 23 [5,3,3,1,1] => 10 [5,3,2,2,1] => 33 [5,3,2,1,1,1] => 1 [5,3,1,1,1,1,1] => 0 [5,2,2,2,2] => 23 [5,2,2,2,1,1] => 3 [5,2,2,1,1,1,1] => 0 [5,2,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1] => 0 [4,4,4,1] => 30 [4,4,3,2] => 30 [4,4,3,1,1] => 6 [4,4,2,2,1] => 21 [4,4,2,1,1,1] => 0 [4,4,1,1,1,1,1] => 0 [4,3,3,3] => 0 [4,3,3,2,1] => 4 [4,3,3,1,1,1] => 0 [4,3,2,2,2] => 14 [4,3,2,2,1,1] => 2 [4,3,2,1,1,1,1] => 0 [4,3,1,1,1,1,1,1] => 0 [4,2,2,2,2,1] => 7 [4,2,2,2,1,1,1] => 0 [4,2,2,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,1] => 0 [3,3,3,2,2] => 0 [3,3,3,2,1,1] => 0 [3,3,3,1,1,1,1] => 0 [3,3,2,2,2,1] => 1 [3,3,2,2,1,1,1] => 0 [3,3,2,1,1,1,1,1] => 0 [3,3,1,1,1,1,1,1,1] => 0 [3,2,2,2,2,2] => 4 [3,2,2,2,2,1,1] => 0 [3,2,2,2,1,1,1,1] => 0 [3,2,2,1,1,1,1,1,1] => 0 [3,2,1,1,1,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2,1] => 1 [2,2,2,2,2,1,1,1] => 0 [2,2,2,2,1,1,1,1,1] => 0 [2,2,2,1,1,1,1,1,1,1] => 0 [2,2,1,1,1,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [14] => 135 [13,1] => 238 [12,2] => 424 [12,1,1] => 127 [11,3] => 528 [11,2,1] => 401 [11,1,1,1] => 20 [10,4] => 616 [10,3,1] => 591 [10,2,2] => 376 [10,2,1,1] => 117 [10,1,1,1,1] => 0 [9,5] => 531 [9,4,1] => 729 [9,3,2] => 607 [9,3,1,1] => 203 [9,2,2,1] => 230 [9,2,1,1,1] => 8 [9,1,1,1,1,1] => 0 [8,6] => 404 [8,5,1] => 622 [8,4,2] => 787 [8,4,1,1] => 266 [8,3,3] => 250 [8,3,2,1] => 382 [8,3,1,1,1] => 20 [8,2,2,2] => 168 [8,2,2,1,1] => 41 [8,2,1,1,1,1] => 0 [8,1,1,1,1,1,1] => 0 [7,7] => 122 [7,6,1] => 383 [7,5,2] => 581 [7,5,1,1] => 215 [7,4,3] => 440 [7,4,2,1] => 474 [7,4,1,1,1] => 28 [7,3,3,1] => 161 [7,3,2,2] => 227 [7,3,2,1,1] => 73 [7,3,1,1,1,1] => 0 [7,2,2,2,1] => 74 [7,2,2,1,1,1] => 1 [7,2,1,1,1,1,1] => 0 [7,1,1,1,1,1,1,1] => 0 [6,6,2] => 262 [6,6,1,1] => 80 [6,5,3] => 286 [6,5,2,1] => 299 [6,5,1,1,1] => 20 [6,4,4] => 197 [6,4,3,1] => 270 [6,4,2,2] => 257 [6,4,2,1,1] => 82 [6,4,1,1,1,1] => 0 [6,3,3,2] => 79 [6,3,3,1,1] => 31 [6,3,2,2,1] => 93 [6,3,2,1,1,1] => 3 [6,3,1,1,1,1,1] => 0 [6,2,2,2,2] => 50 [6,2,2,2,1,1] => 8 [6,2,2,1,1,1,1] => 0 [6,2,1,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1,1] => 0 [5,5,4] => 64 [5,5,3,1] => 105 [5,5,2,2] => 86 [5,5,2,1,1] => 40 [5,5,1,1,1,1] => 1 [5,4,4,1] => 107 [5,4,3,2] => 118 [5,4,3,1,1] => 44 [5,4,2,2,1] => 80 [5,4,2,1,1,1] => 3 [5,4,1,1,1,1,1] => 0 [5,3,3,3] => 4 [5,3,3,2,1] => 24 [5,3,3,1,1,1] => 2 [5,3,2,2,2] => 40 [5,3,2,2,1,1] => 10 [5,3,2,1,1,1,1] => 0 [5,3,1,1,1,1,1,1] => 0 [5,2,2,2,2,1] => 16 [5,2,2,2,1,1,1] => 0 [5,2,2,1,1,1,1,1] => 0 [5,2,1,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1,1] => 0 [4,4,4,2] => 47 [4,4,4,1,1] => 10 [4,4,3,3] => 10 [4,4,3,2,1] => 24 [4,4,3,1,1,1] => 0 [4,4,2,2,2] => 27 [4,4,2,2,1,1] => 5 [4,4,2,1,1,1,1] => 0 [4,4,1,1,1,1,1,1] => 0 [4,3,3,3,1] => 0 [4,3,3,2,2] => 5 [4,3,3,2,1,1] => 1 [4,3,3,1,1,1,1] => 0 [4,3,2,2,2,1] => 10 [4,3,2,2,1,1,1] => 0 [4,3,2,1,1,1,1,1] => 0 [4,3,1,1,1,1,1,1,1] => 0 [4,2,2,2,2,2] => 11 [4,2,2,2,2,1,1] => 1 [4,2,2,2,1,1,1,1] => 0 [4,2,2,1,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,2] => 0 [3,3,3,3,1,1] => 0 [3,3,3,2,2,1] => 0 [3,3,3,2,1,1,1] => 0 [3,3,3,1,1,1,1,1] => 0 [3,3,2,2,2,2] => 2 [3,3,2,2,2,1,1] => 0 [3,3,2,2,1,1,1,1] => 0 [3,3,2,1,1,1,1,1,1] => 0 [3,3,1,1,1,1,1,1,1,1] => 0 [3,2,2,2,2,2,1] => 2 [3,2,2,2,2,1,1,1] => 0 [3,2,2,2,1,1,1,1,1] => 0 [3,2,2,1,1,1,1,1,1,1] => 0 [3,2,1,1,1,1,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2,2] => 2 [2,2,2,2,2,2,1,1] => 0 [2,2,2,2,2,1,1,1,1] => 0 [2,2,2,2,1,1,1,1,1,1] => 0 [2,2,2,1,1,1,1,1,1,1,1] => 0 [2,2,1,1,1,1,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [15] => 176 [14,1] => 332 [13,2] => 603 [13,1,1] => 193 [12,3] => 803 [12,2,1] => 619 [12,1,1,1] => 34 [11,4] => 962 [11,3,1] => 960 [11,2,2] => 591 [11,2,1,1] => 204 [11,1,1,1,1] => 1 [10,5] => 928 [10,4,1] => 1271 [10,3,2] => 1052 [10,3,1,1] => 373 [10,2,2,1] => 399 [10,2,1,1,1] => 17 [10,1,1,1,1,1] => 0 [9,6] => 767 [9,5,1] => 1194 [9,4,2] => 1444 [9,4,1,1] => 529 [9,3,3] => 484 [9,3,2,1] => 729 [9,3,1,1,1] => 47 [9,2,2,2] => 290 [9,2,2,1,1] => 83 [9,2,1,1,1,1] => 0 [9,1,1,1,1,1,1] => 0 [8,7] => 416 [8,6,1] => 927 [8,5,2] => 1300 [8,5,1,1] => 493 [8,4,3] => 931 [8,4,2,1] => 1013 [8,4,1,1,1] => 69 [8,3,3,1] => 359 [8,3,2,2] => 471 [8,3,2,1,1] => 166 [8,3,1,1,1,1] => 1 [8,2,2,2,1] => 145 [8,2,2,1,1,1] => 3 [8,2,1,1,1,1,1] => 0 [8,1,1,1,1,1,1,1] => 0 [7,7,1] => 312 [7,6,2] => 814 [7,6,1,1] => 309 [7,5,3] => 771 [7,5,2,1] => 814 [7,5,1,1,1] => 70 [7,4,4] => 447 [7,4,3,1] => 680 [7,4,2,2] => 585 [7,4,2,1,1] => 221 [7,4,1,1,1,1] => 1 [7,3,3,2] => 208 [7,3,3,1,1] => 90 [7,3,2,2,1] => 216 [7,3,2,1,1,1] => 10 [7,3,1,1,1,1,1] => 0 [7,2,2,2,2] => 95 [7,2,2,2,1,1] => 20 [7,2,2,1,1,1,1] => 0 [7,2,1,1,1,1,1,1] => 0 [7,1,1,1,1,1,1,1,1] => 0 [6,6,3] => 366 [6,6,2,1] => 339 [6,6,1,1,1] => 18 [6,5,4] => 336 [6,5,3,1] => 471 [6,5,2,2] => 379 [6,5,2,1,1] => 154 [6,5,1,1,1,1] => 2 [6,4,4,1] => 329 [6,4,3,2] => 383 [6,4,3,1,1] => 145 [6,4,2,2,1] => 246 [6,4,2,1,1,1] => 11 [6,4,1,1,1,1,1] => 0 [6,3,3,3] => 20 [6,3,3,2,1] => 84 [6,3,3,1,1,1] => 8 [6,3,2,2,2] => 110 [6,3,2,2,1,1] => 30 [6,3,2,1,1,1,1] => 0 [6,3,1,1,1,1,1,1] => 0 [6,2,2,2,2,1] => 37 [6,2,2,2,1,1,1] => 0 [6,2,2,1,1,1,1,1] => 0 [6,2,1,1,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1,1,1] => 0 [5,5,5] => 20 [5,5,4,1] => 136 [5,5,3,2] => 144 [5,5,3,1,1] => 79 [5,5,2,2,1] => 92 [5,5,2,1,1,1] => 10 [5,5,1,1,1,1,1] => 0 [5,4,4,2] => 170 [5,4,4,1,1] => 59 [5,4,3,3] => 52 [5,4,3,2,1] => 122 [5,4,3,1,1,1] => 8 [5,4,2,2,2] => 91 [5,4,2,2,1,1] => 27 [5,4,2,1,1,1,1] => 0 [5,4,1,1,1,1,1,1] => 0 [5,3,3,3,1] => 6 [5,3,3,2,2] => 23 [5,3,3,2,1,1] => 11 [5,3,3,1,1,1,1] => 0 [5,3,2,2,2,1] => 33 [5,3,2,2,1,1,1] => 1 [5,3,2,1,1,1,1,1] => 0 [5,3,1,1,1,1,1,1,1] => 0 [5,2,2,2,2,2] => 23 [5,2,2,2,2,1,1] => 3 [5,2,2,2,1,1,1,1] => 0 [5,2,2,1,1,1,1,1,1] => 0 [5,2,1,1,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1,1,1] => 0 [4,4,4,3] => 38 [4,4,4,2,1] => 40 [4,4,4,1,1,1] => 0 [4,4,3,3,1] => 8 [4,4,3,2,2] => 30 [4,4,3,2,1,1] => 6 [4,4,3,1,1,1,1] => 0 [4,4,2,2,2,1] => 21 [4,4,2,2,1,1,1] => 0 [4,4,2,1,1,1,1,1] => 0 [4,4,1,1,1,1,1,1,1] => 0 [4,3,3,3,2] => 0 [4,3,3,3,1,1] => 0 [4,3,3,2,2,1] => 4 [4,3,3,2,1,1,1] => 0 [4,3,3,1,1,1,1,1] => 0 [4,3,2,2,2,2] => 14 [4,3,2,2,2,1,1] => 2 [4,3,2,2,1,1,1,1] => 0 [4,3,2,1,1,1,1,1,1] => 0 [4,3,1,1,1,1,1,1,1,1] => 0 [4,2,2,2,2,2,1] => 7 [4,2,2,2,2,1,1,1] => 0 [4,2,2,2,1,1,1,1,1] => 0 [4,2,2,1,1,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,3] => 0 [3,3,3,3,2,1] => 0 [3,3,3,3,1,1,1] => 0 [3,3,3,2,2,2] => 0 [3,3,3,2,2,1,1] => 0 [3,3,3,2,1,1,1,1] => 0 [3,3,3,1,1,1,1,1,1] => 0 [3,3,2,2,2,2,1] => 1 [3,3,2,2,2,1,1,1] => 0 [3,3,2,2,1,1,1,1,1] => 0 [3,3,2,1,1,1,1,1,1,1] => 0 [3,3,1,1,1,1,1,1,1,1,1] => 0 [3,2,2,2,2,2,2] => 4 [3,2,2,2,2,2,1,1] => 0 [3,2,2,2,2,1,1,1,1] => 0 [3,2,2,2,1,1,1,1,1,1] => 0 [3,2,2,1,1,1,1,1,1,1,1] => 0 [3,2,1,1,1,1,1,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2,2,1] => 1 [2,2,2,2,2,2,1,1,1] => 0 [2,2,2,2,2,1,1,1,1,1] => 0 [2,2,2,2,1,1,1,1,1,1,1] => 0 [2,2,2,1,1,1,1,1,1,1,1,1] => 0 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [16] => 231 [15,1] => 453 [14,2] => 857 [14,1,1] => 285 [13,3] => 1178 [13,2,1] => 932 [13,1,1,1] => 60 [12,4] => 1496 [12,3,1] => 1526 [12,2,2] => 919 [12,2,1,1] => 338 [12,1,1,1,1] => 2 [11,5] => 1512 [11,4,1] => 2105 [11,3,2] => 1740 [11,3,1,1] => 662 [11,2,2,1] => 663 [11,2,1,1,1] => 37 [11,1,1,1,1,1] => 0 [10,6] => 1401 [10,5,1] => 2189 [10,4,2] => 2571 [10,4,1,1] => 986 [10,3,3] => 885 [10,3,2,1] => 1332 [10,3,1,1,1] => 97 [10,2,2,2] => 497 [10,2,2,1,1] => 157 [10,2,1,1,1,1] => 0 [10,1,1,1,1,1,1] => 0 [9,7] => 915 [9,6,1] => 1893 [9,5,2] => 2557 [9,5,1,1] => 1034 [9,4,3] => 1800 [9,4,2,1] => 1988 [9,4,1,1,1] => 161 [9,3,3,1] => 743 [9,3,2,2] => 891 [9,3,2,1,1] => 350 [9,3,1,1,1,1] => 3 [9,2,2,2,1] => 267 [9,2,2,1,1,1] => 9 [9,2,1,1,1,1,1] => 0 [9,1,1,1,1,1,1,1] => 0 [8,8] => 363 [8,7,1] => 1067 [8,6,2] => 2043 [8,6,1,1] => 803 [8,5,3] => 1815 [8,5,2,1] => 1909 [8,5,1,1,1] => 176 [8,4,4] => 958 [8,4,3,1] => 1526 [8,4,2,2] => 1267 [8,4,2,1,1] => 516 [8,4,1,1,1,1] => 5 [8,3,3,2] => 483 [8,3,3,1,1] => 218 [8,3,2,2,1] => 470 [8,3,2,1,1,1] => 28 [8,3,1,1,1,1,1] => 0 [8,2,2,2,2] => 180 [8,2,2,2,1,1] => 43 [8,2,2,1,1,1,1] => 0 [8,2,1,1,1,1,1,1] => 0 [8,1,1,1,1,1,1,1,1] => 0 [7,7,2] => 692 [7,7,1,1] => 312 [7,6,3] => 1220 [7,6,2,1] => 1208 [7,6,1,1,1] => 107 [7,5,4] => 944 [7,5,3,1] => 1384 [7,5,2,2] => 1015 [7,5,2,1,1] => 469 [7,5,1,1,1,1] => 8 [7,4,4,1] => 817 [7,4,3,2] => 979 [7,4,3,1,1] => 417 [7,4,2,2,1] => 606 [7,4,2,1,1,1] => 39 [7,4,1,1,1,1,1] => 0 [7,3,3,3] => 73 [7,3,3,2,1] => 236 [7,3,3,1,1,1] => 23 [7,3,2,2,2] => 245 [7,3,2,2,1,1] => 81 [7,3,2,1,1,1,1] => 0 [7,3,1,1,1,1,1,1] => 0 [7,2,2,2,2,1] => 76 [7,2,2,2,1,1,1] => 1 [7,2,2,1,1,1,1,1] => 0 [7,2,1,1,1,1,1,1,1] => 0 [7,1,1,1,1,1,1,1,1,1] => 0 [6,6,4] => 490 [6,6,3,1] => 602 [6,6,2,2] => 452 [6,6,2,1,1] => 173 [6,6,1,1,1,1] => 1 [6,5,5] => 178 [6,5,4,1] => 665 [6,5,3,2] => 702 [6,5,3,1,1] => 324 [6,5,2,2,1] => 410 [6,5,2,1,1,1] => 35 [6,5,1,1,1,1,1] => 0 [6,4,4,2] => 542 [6,4,4,1,1] => 202 [6,4,3,3] => 190 [6,4,3,2,1] => 422 [6,4,3,1,1,1] => 34 [6,4,2,2,2] => 278 [6,4,2,2,1,1] => 90 [6,4,2,1,1,1,1] => 0 [6,4,1,1,1,1,1,1] => 0 [6,3,3,3,1] => 28 [6,3,3,2,2] => 85 [6,3,3,2,1,1] => 41 [6,3,3,1,1,1,1] => 1 [6,3,2,2,2,1] => 94 [6,3,2,2,1,1,1] => 3 [6,3,2,1,1,1,1,1] => 0 [6,3,1,1,1,1,1,1,1] => 0 [6,2,2,2,2,2] => 50 [6,2,2,2,2,1,1] => 8 [6,2,2,2,1,1,1,1] => 0 [6,2,2,1,1,1,1,1,1] => 0 [6,2,1,1,1,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1,1,1,1] => 0 [5,5,5,1] => 64 [5,5,4,2] => 221 [5,5,4,1,1] => 120 [5,5,3,3] => 83 [5,5,3,2,1] => 188 [5,5,3,1,1,1] => 27 [5,5,2,2,2] => 92 [5,5,2,2,1,1] => 43 [5,5,2,1,1,1,1] => 1 [5,5,1,1,1,1,1,1] => 0 [5,4,4,3] => 148 [5,4,4,2,1] => 186 [5,4,4,1,1,1] => 11 [5,4,3,3,1] => 65 [5,4,3,2,2] => 127 [5,4,3,2,1,1] => 51 [5,4,3,1,1,1,1] => 0 [5,4,2,2,2,1] => 80 [5,4,2,2,1,1,1] => 3 [5,4,2,1,1,1,1,1] => 0 [5,4,1,1,1,1,1,1,1] => 0 [5,3,3,3,2] => 4 [5,3,3,3,1,1] => 4 [5,3,3,2,2,1] => 24 [5,3,3,2,1,1,1] => 2 [5,3,3,1,1,1,1,1] => 0 [5,3,2,2,2,2] => 40 [5,3,2,2,2,1,1] => 10 [5,3,2,2,1,1,1,1] => 0 [5,3,2,1,1,1,1,1,1] => 0 [5,3,1,1,1,1,1,1,1,1] => 0 [5,2,2,2,2,2,1] => 16 [5,2,2,2,2,1,1,1] => 0 [5,2,2,2,1,1,1,1,1] => 0 [5,2,2,1,1,1,1,1,1,1] => 0 [5,2,1,1,1,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1,1,1,1] => 0 [4,4,4,4] => 38 [4,4,4,3,1] => 37 [4,4,4,2,2] => 50 [4,4,4,2,1,1] => 10 [4,4,4,1,1,1,1] => 0 [4,4,3,3,2] => 10 [4,4,3,3,1,1] => 2 [4,4,3,2,2,1] => 24 [4,4,3,2,1,1,1] => 0 [4,4,3,1,1,1,1,1] => 0 [4,4,2,2,2,2] => 27 [4,4,2,2,2,1,1] => 5 [4,4,2,2,1,1,1,1] => 0 [4,4,2,1,1,1,1,1,1] => 0 [4,4,1,1,1,1,1,1,1,1] => 0 [4,3,3,3,3] => 0 [4,3,3,3,2,1] => 0 [4,3,3,3,1,1,1] => 0 [4,3,3,2,2,2] => 5 [4,3,3,2,2,1,1] => 1 [4,3,3,2,1,1,1,1] => 0 [4,3,3,1,1,1,1,1,1] => 0 [4,3,2,2,2,2,1] => 10 [4,3,2,2,2,1,1,1] => 0 [4,3,2,2,1,1,1,1,1] => 0 [4,3,2,1,1,1,1,1,1,1] => 0 [4,3,1,1,1,1,1,1,1,1,1] => 0 [4,2,2,2,2,2,2] => 11 [4,2,2,2,2,2,1,1] => 1 [4,2,2,2,2,1,1,1,1] => 0 [4,2,2,2,1,1,1,1,1,1] => 0 [4,2,2,1,1,1,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,3,1] => 0 [3,3,3,3,2,2] => 0 [3,3,3,3,2,1,1] => 0 [3,3,3,3,1,1,1,1] => 0 [3,3,3,2,2,2,1] => 0 [3,3,3,2,2,1,1,1] => 0 [3,3,3,2,1,1,1,1,1] => 0 [3,3,3,1,1,1,1,1,1,1] => 0 [3,3,2,2,2,2,2] => 2 [3,3,2,2,2,2,1,1] => 0 [3,3,2,2,2,1,1,1,1] => 0 [3,3,2,2,1,1,1,1,1,1] => 0 [3,3,2,1,1,1,1,1,1,1,1] => 0 [3,3,1,1,1,1,1,1,1,1,1,1] => 0 [3,2,2,2,2,2,2,1] => 2 [3,2,2,2,2,2,1,1,1] => 0 [3,2,2,2,2,1,1,1,1,1] => 0 [3,2,2,2,1,1,1,1,1,1,1] => 0 [3,2,2,1,1,1,1,1,1,1,1,1] => 0 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2,2,2] => 2 [2,2,2,2,2,2,2,1,1] => 0 [2,2,2,2,2,2,1,1,1,1] => 0 [2,2,2,2,2,1,1,1,1,1,1] => 0 [2,2,2,2,1,1,1,1,1,1,1,1] => 0 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [17] => 297 [16,1] => 618 [15,2] => 1191 [15,1,1] => 415 [14,3] => 1718 [14,2,1] => 1382 [14,1,1,1] => 97 [13,4] => 2242 [13,3,1] => 2360 [13,2,2] => 1388 [13,2,1,1] => 551 [13,1,1,1,1] => 5 [12,5] => 2432 [12,4,1] => 3410 [12,3,2] => 2816 [12,3,1,1] => 1117 [12,2,2,1] => 1080 [12,2,1,1,1] => 70 [12,1,1,1,1,1] => 0 [11,6] => 2362 [11,5,1] => 3772 [11,4,2] => 4348 [11,4,1,1] => 1765 [11,3,3] => 1544 [11,3,2,1] => 2328 [11,3,1,1,1] => 196 [11,2,2,2] => 814 [11,2,2,1,1] => 286 [11,2,1,1,1,1] => 1 [11,1,1,1,1,1,1] => 0 [10,7] => 1833 [10,6,1] => 3628 [10,5,2] => 4796 [10,5,1,1] => 2007 [10,4,3] => 3329 [10,4,2,1] => 3720 [10,4,1,1,1] => 333 [10,3,3,1] => 1430 [10,3,2,2] => 1634 [10,3,2,1,1] => 688 [10,3,1,1,1,1] => 8 [10,2,2,2,1] => 479 [10,2,2,1,1,1] => 20 [10,2,1,1,1,1,1] => 0 [10,1,1,1,1,1,1,1] => 0 [9,8] => 1022 [9,7,1] => 2504 [9,6,2] => 4289 [9,6,1,1] => 1804 [9,5,3] => 3758 [9,5,2,1] => 3991 [9,5,1,1,1] => 413 [9,4,4] => 1863 [9,4,3,1] => 3148 [9,4,2,2] => 2489 [9,4,2,1,1] => 1114 [9,4,1,1,1,1] => 16 [9,3,3,2] => 1022 [9,3,3,1,1] => 483 [9,3,2,2,1] => 942 [9,3,2,1,1,1] => 70 [9,3,1,1,1,1,1] => 0 [9,2,2,2,2] => 319 [9,2,2,2,1,1] => 90 [9,2,2,1,1,1,1] => 0 [9,2,1,1,1,1,1,1] => 0 [9,1,1,1,1,1,1,1,1] => 0 [8,8,1] => 958 [8,7,2] => 2466 [8,7,1,1] => 1070 [8,6,3] => 3200 [8,6,2,1] => 3207 [8,6,1,1,1] => 315 [8,5,4] => 2308 [8,5,3,1] => 3401 [8,5,2,2] => 2431 [8,5,2,1,1] => 1172 [8,5,1,1,1,1] => 26 [8,4,4,1] => 1853 [8,4,3,2] => 2266 [8,4,3,1,1] => 1017 [8,4,2,2,1] => 1379 [8,4,2,1,1,1] => 108 [8,4,1,1,1,1,1] => 0 [8,3,3,3] => 192 [8,3,3,2,1] => 577 [8,3,3,1,1,1] => 65 [8,3,2,2,2] => 524 [8,3,2,2,1,1] => 189 [8,3,2,1,1,1,1] => 1 [8,3,1,1,1,1,1,1] => 0 [8,2,2,2,2,1] => 151 [8,2,2,2,1,1,1] => 3 [8,2,2,1,1,1,1,1] => 0 [8,2,1,1,1,1,1,1,1] => 0 [8,1,1,1,1,1,1,1,1,1] => 0 [7,7,3] => 1129 [7,7,2,1] => 1175 [7,7,1,1,1] => 143 [7,6,4] => 1697 [7,6,3,1] => 2298 [7,6,2,2] => 1555 [7,6,2,1,1] => 742 [7,6,1,1,1,1] => 13 [7,5,5] => 596 [7,5,4,1] => 2010 [7,5,3,2] => 2099 [7,5,3,1,1] => 1036 [7,5,2,2,1] => 1178 [7,5,2,1,1,1] => 121 [7,5,1,1,1,1,1] => 0 [7,4,4,2] => 1370 [7,4,4,1,1] => 576 [7,4,3,3] => 556 [7,4,3,2,1] => 1169 [7,4,3,1,1,1] => 114 [7,4,2,2,2] => 663 [7,4,2,2,1,1] => 255 [7,4,2,1,1,1,1] => 1 [7,4,1,1,1,1,1,1] => 0 [7,3,3,3,1] => 104 [7,3,3,2,2] => 236 [7,3,3,2,1,1] => 122 [7,3,3,1,1,1,1] => 2 [7,3,2,2,2,1] => 226 [7,3,2,2,1,1,1] => 11 [7,3,2,1,1,1,1,1] => 0 [7,3,1,1,1,1,1,1,1] => 0 [7,2,2,2,2,2] => 96 [7,2,2,2,2,1,1] => 20 [7,2,2,2,1,1,1,1] => 0 [7,2,2,1,1,1,1,1,1] => 0 [7,2,1,1,1,1,1,1,1,1] => 0 [7,1,1,1,1,1,1,1,1,1,1] => 0 [6,6,5] => 438 [6,6,4,1] => 963 [6,6,3,2] => 959 [6,6,3,1,1] => 403 [6,6,2,2,1] => 503 [6,6,2,1,1,1] => 38 [6,6,1,1,1,1,1] => 0 [6,5,5,1] => 427 [6,5,4,2] => 1146 [6,5,4,1,1] => 540 [6,5,3,3] => 427 [6,5,3,2,1] => 898 [6,5,3,1,1,1] => 111 [6,5,2,2,2] => 438 [6,5,2,2,1,1] => 186 [6,5,2,1,1,1,1] => 3 [6,5,1,1,1,1,1,1] => 0 [6,4,4,3] => 498 [6,4,4,2,1] => 645 [6,4,4,1,1,1] => 49 [6,4,3,3,1] => 255 [6,4,3,2,2] => 449 [6,4,3,2,1,1] => 198 [6,4,3,1,1,1,1] => 3 [6,4,2,2,2,1] => 253 [6,4,2,2,1,1,1] => 11 [6,4,2,1,1,1,1,1] => 0 [6,4,1,1,1,1,1,1,1] => 0 [6,3,3,3,2] => 24 [6,3,3,3,1,1] => 22 [6,3,3,2,2,1] => 88 [6,3,3,2,1,1,1] => 10 [6,3,3,1,1,1,1,1] => 0 [6,3,2,2,2,2] => 110 [6,3,2,2,2,1,1] => 30 [6,3,2,2,1,1,1,1] => 0 [6,3,2,1,1,1,1,1,1] => 0 [6,3,1,1,1,1,1,1,1,1] => 0 [6,2,2,2,2,2,1] => 37 [6,2,2,2,2,1,1,1] => 0 [6,2,2,2,1,1,1,1,1] => 0 [6,2,2,1,1,1,1,1,1,1] => 0 [6,2,1,1,1,1,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1,1,1,1,1] => 0 [5,5,5,2] => 109 [5,5,5,1,1] => 88 [5,5,4,3] => 215 [5,5,4,2,1] => 322 [5,5,4,1,1,1] => 50 [5,5,3,3,1] => 137 [5,5,3,2,2] => 174 [5,5,3,2,1,1] => 109 [5,5,3,1,1,1,1] => 3 [5,5,2,2,2,1] => 93 [5,5,2,2,1,1,1] => 10 [5,5,2,1,1,1,1,1] => 0 [5,5,1,1,1,1,1,1,1] => 0 [5,4,4,4] => 131 [5,4,4,3,1] => 196 [5,4,4,2,2] => 206 [5,4,4,2,1,1] => 77 [5,4,4,1,1,1,1] => 0 [5,4,3,3,2] => 68 [5,4,3,3,1,1] => 34 [5,4,3,2,2,1] => 124 [5,4,3,2,1,1,1] => 8 [5,4,3,1,1,1,1,1] => 0 [5,4,2,2,2,2] => 91 [5,4,2,2,2,1,1] => 27 [5,4,2,2,1,1,1,1] => 0 [5,4,2,1,1,1,1,1,1] => 0 [5,4,1,1,1,1,1,1,1,1] => 0 [5,3,3,3,3] => 0 [5,3,3,3,2,1] => 6 [5,3,3,3,1,1,1] => 1 [5,3,3,2,2,2] => 23 [5,3,3,2,2,1,1] => 11 [5,3,3,2,1,1,1,1] => 0 [5,3,3,1,1,1,1,1,1] => 0 [5,3,2,2,2,2,1] => 33 [5,3,2,2,2,1,1,1] => 1 [5,3,2,2,1,1,1,1,1] => 0 [5,3,2,1,1,1,1,1,1,1] => 0 [5,3,1,1,1,1,1,1,1,1,1] => 0 [5,2,2,2,2,2,2] => 23 [5,2,2,2,2,2,1,1] => 3 [5,2,2,2,2,1,1,1,1] => 0 [5,2,2,2,1,1,1,1,1,1] => 0 [5,2,2,1,1,1,1,1,1,1,1] => 0 [5,2,1,1,1,1,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [4,4,4,4,1] => 46 [4,4,4,3,2] => 50 [4,4,4,3,1,1] => 10 [4,4,4,2,2,1] => 40 [4,4,4,2,1,1,1] => 0 [4,4,4,1,1,1,1,1] => 0 [4,4,3,3,3] => 0 [4,4,3,3,2,1] => 8 [4,4,3,3,1,1,1] => 0 [4,4,3,2,2,2] => 30 [4,4,3,2,2,1,1] => 6 [4,4,3,2,1,1,1,1] => 0 [4,4,3,1,1,1,1,1,1] => 0 [4,4,2,2,2,2,1] => 21 [4,4,2,2,2,1,1,1] => 0 [4,4,2,2,1,1,1,1,1] => 0 [4,4,2,1,1,1,1,1,1,1] => 0 [4,4,1,1,1,1,1,1,1,1,1] => 0 [4,3,3,3,3,1] => 0 [4,3,3,3,2,2] => 0 [4,3,3,3,2,1,1] => 0 [4,3,3,3,1,1,1,1] => 0 [4,3,3,2,2,2,1] => 4 [4,3,3,2,2,1,1,1] => 0 [4,3,3,2,1,1,1,1,1] => 0 [4,3,3,1,1,1,1,1,1,1] => 0 [4,3,2,2,2,2,2] => 14 [4,3,2,2,2,2,1,1] => 2 [4,3,2,2,2,1,1,1,1] => 0 [4,3,2,2,1,1,1,1,1,1] => 0 [4,3,2,1,1,1,1,1,1,1,1] => 0 [4,3,1,1,1,1,1,1,1,1,1,1] => 0 [4,2,2,2,2,2,2,1] => 7 [4,2,2,2,2,2,1,1,1] => 0 [4,2,2,2,2,1,1,1,1,1] => 0 [4,2,2,2,1,1,1,1,1,1,1] => 0 [4,2,2,1,1,1,1,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,3,2] => 0 [3,3,3,3,3,1,1] => 0 [3,3,3,3,2,2,1] => 0 [3,3,3,3,2,1,1,1] => 0 [3,3,3,3,1,1,1,1,1] => 0 [3,3,3,2,2,2,2] => 0 [3,3,3,2,2,2,1,1] => 0 [3,3,3,2,2,1,1,1,1] => 0 [3,3,3,2,1,1,1,1,1,1] => 0 [3,3,3,1,1,1,1,1,1,1,1] => 0 [3,3,2,2,2,2,2,1] => 1 [3,3,2,2,2,2,1,1,1] => 0 [3,3,2,2,2,1,1,1,1,1] => 0 [3,3,2,2,1,1,1,1,1,1,1] => 0 [3,3,2,1,1,1,1,1,1,1,1,1] => 0 [3,3,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,2,2,2,2,2,2,2] => 4 [3,2,2,2,2,2,2,1,1] => 0 [3,2,2,2,2,2,1,1,1,1] => 0 [3,2,2,2,2,1,1,1,1,1,1] => 0 [3,2,2,2,1,1,1,1,1,1,1,1] => 0 [3,2,2,1,1,1,1,1,1,1,1,1,1] => 0 ----------------------------------------------------------------------------- Created: Sep 26, 2020 at 23:09 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 26, 2020 at 23:09 by Martin Rubey