***************************************************************************** * 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: 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 ----------------------------------------------------------------------------- Last Updated: Sep 27, 2020 at 00:18 by Martin Rubey