***************************************************************************** * 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: St001599 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(mu): s = SymmetricFunctions(QQ).s() A = CombinatorialSpecies() X = species.SingletonSpecies() E = species.SetSpecies() A.define(X*E(A)) F = A.cycle_index_series() return F.coefficient(mu.size()).scalar(s(mu)) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 1 [1,1] => 1 [3] => 2 [2,1] => 3 [1,1,1] => 1 [4] => 4 [3,1] => 9 [2,2] => 5 [2,1,1] => 7 [1,1,1,1] => 2 [5] => 9 [4,1] => 26 [3,2] => 28 [3,1,1] => 30 [2,2,1] => 24 [2,1,1,1] => 17 [1,1,1,1,1] => 4 [6] => 20 [5,1] => 75 [4,2] => 114 [4,1,1] => 117 [3,3] => 59 [3,2,1] => 170 [3,1,1,1] => 96 [2,2,2] => 49 [2,2,1,1] => 83 [2,1,1,1,1] => 42 [1,1,1,1,1,1] => 8 [7] => 48 [6,1] => 214 [5,2] => 421 [5,1,1] => 419 [4,3] => 382 [4,2,1] => 874 [4,1,1,1] => 459 [3,3,1] => 493 [3,2,2] => 474 [3,2,1,1] => 745 [3,1,1,1,1] => 294 [2,2,2,1] => 281 [2,2,1,1,1] => 261 [2,1,1,1,1,1] => 104 [1,1,1,1,1,1,1] => 16 [8] => 115 [7,1] => 612 [6,2] => 1462 [6,1,1] => 1446 [5,3] => 1833 [5,2,1] => 3875 [5,1,1,1] => 1966 [4,4] => 868 [4,3,1] => 3930 [4,2,2] => 3014 [4,2,1,1] => 4619 [4,1,1,1,1] => 1657 [3,3,2] => 2154 [3,3,1,1] => 2742 [3,2,2,1] => 3309 [3,2,1,1,1] => 2847 [3,1,1,1,1,1] => 863 [2,2,2,2] => 615 [2,2,2,1,1] => 1181 [2,2,1,1,1,1] => 789 [2,1,1,1,1,1,1] => 257 [1,1,1,1,1,1,1,1] => 34 [9] => 286 [8,1] => 1747 [7,2] => 4918 [7,1,1] => 4834 [6,3] => 7733 [6,2,1] => 15795 [6,1,1,1] => 7881 [5,4] => 6309 [5,3,1] => 22276 [5,2,2] => 15880 [5,2,1,1] => 23968 [5,1,1,1,1] => 8243 [4,4,1] => 11068 [4,3,2] => 20851 [4,3,1,1] => 25758 [4,2,2,1] => 24878 [4,2,1,1,1] => 20609 [4,1,1,1,1,1] => 5646 [3,3,3] => 4901 [3,3,2,1] => 18597 [3,3,1,1,1] => 12607 [3,2,2,2] => 8857 [3,2,2,1,1] => 16474 [3,2,1,1,1,1] => 10041 [3,1,1,1,1,1,1] => 2473 [2,2,2,2,1] => 4016 [2,2,2,1,1,1] => 4378 [2,2,1,1,1,1,1] => 2313 [2,1,1,1,1,1,1,1] => 637 [1,1,1,1,1,1,1,1,1] => 75 [10] => 719 [9,1] => 4995 [8,2] => 16146 [8,1,1] => 15857 [7,3] => 30362 [7,2,1] => 60900 [7,1,1,1] => 30112 [6,4] => 33498 [6,3,1] => 108412 [6,2,2] => 74709 [6,2,1,1] => 111911 [6,1,1,1,1] => 37600 [5,5] => 15006 [5,4,1] => 93468 [5,3,2] => 138409 [5,3,1,1] => 168245 [5,2,2,1] => 150801 [5,2,1,1,1] => 122417 [5,1,1,1,1,1] => 31950 [4,4,2] => 74669 [4,4,1,1] => 85834 [4,3,3] => 60063 [4,3,2,1] => 209063 [4,3,1,1,1] => 136189 [4,2,2,2] => 77965 [4,2,2,1,1] => 142719 [4,2,1,1,1,1] => 83113 [4,1,1,1,1,1,1] => 18455 [3,3,3,1] => 54317 [3,3,2,2] => 63287 [3,3,2,1,1] => 109553 [3,3,1,1,1,1] => 51744 [3,2,2,2,1] => 67184 [3,2,2,1,1,1] => 70417 [3,2,1,1,1,1,1] => 33588 [3,1,1,1,1,1,1,1] => 6994 [2,2,2,2,2] => 9137 [2,2,2,2,1,1] => 19047 [2,2,2,1,1,1,1] => 15109 [2,2,1,1,1,1,1,1] => 6619 [2,1,1,1,1,1,1,1,1] => 1586 [1,1,1,1,1,1,1,1,1,1] => 166 [11] => 1842 [10,1] => 14294 [9,2] => 52188 [9,1,1] => 51198 [8,3] => 113682 [8,2,1] => 225817 [8,1,1,1] => 111100 [7,4] => 155126 [7,3,1] => 481703 [7,2,2] => 326253 [7,2,1,1] => 486387 [7,1,1,1,1] => 161328 [6,5] => 117380 [6,4,1] => 565246 [6,3,2] => 768853 [6,3,1,1] => 926155 [6,2,2,1] => 802176 [6,2,1,1,1] => 643560 [6,1,1,1,1,1] => 163526 [5,5,1] => 259844 [5,4,2] => 730560 [5,4,1,1] => 825653 [5,3,3] => 471677 [5,3,2,1] => 1577580 [5,3,1,1,1] => 1006100 [5,2,2,2] => 539526 [5,2,2,1,1] => 978015 [5,2,1,1,1,1] => 555595 [5,1,1,1,1,1,1] => 117102 [4,4,3] => 319567 [4,4,2,1] => 872849 [4,4,1,1,1] => 522151 [4,3,3,1] => 762112 [4,3,2,2] => 823458 [4,3,2,1,1] => 1400739 [4,3,1,1,1,1] => 632258 [4,2,2,2,1] => 672645 [4,2,2,1,1,1] => 689628 [4,2,1,1,1,1,1] => 312922 [4,1,1,1,1,1,1,1] => 58522 [3,3,3,2] => 275496 [3,3,3,1,1] => 382999 [3,3,2,2,1] => 559655 [3,3,2,1,1,1] => 538355 [3,3,1,1,1,1,1] => 197143 [3,2,2,2,2] => 177253 [3,2,2,2,1,1] => 362854 [3,2,2,1,1,1,1] => 274761 [3,2,1,1,1,1,1,1] => 108250 [3,1,1,1,1,1,1,1,1] => 19561 [2,2,2,2,2,1] => 64977 [2,2,2,2,1,1,1] => 78474 [2,2,2,1,1,1,1,1] => 49699 [2,2,1,1,1,1,1,1,1] => 18650 [2,1,1,1,1,1,1,1,1,1] => 3959 [1,1,1,1,1,1,1,1,1,1,1] => 370 [12] => 4766 [11,1] => 40967 [10,2] => 166593 [10,1,1] => 163477 [9,3] => 411740 [9,2,1] => 813242 [9,1,1,1] => 398984 [8,4] => 662870 [8,3,1] => 2013446 [8,2,2] => 1350027 [8,2,1,1] => 2007267 [8,1,1,1,1] => 660569 [7,5] => 669168 [7,4,1] => 2932280 [7,3,2] => 3832294 [7,3,1,1] => 4591051 [7,2,2,1] => 3904901 [7,2,1,1,1] => 3110383 [7,1,1,1,1,1] => 777944 [6,6] => 287646 [6,5,1] => 2292196 [6,4,2] => 4998273 [6,4,1,1] => 5594484 [6,3,3] => 2996417 [6,3,2,1] => 9806438 [6,3,1,1,1] => 6176275 [6,2,2,2] => 3218526 [6,2,2,1,1] => 5799947 [6,2,1,1,1,1] => 3246181 [6,1,1,1,1,1,1] => 664489 [5,5,2] => 2393038 [5,5,1,1] => 2616024 [5,4,3] => 3665196 [5,4,2,1] => 9615650 [5,4,1,1,1] => 5629097 [5,3,3,1] => 6733253 [5,3,2,2] => 7027859 [5,3,2,1,1] => 11832377 [5,3,1,1,1,1] => 5208603 [5,2,2,2,1] => 5207109 [5,2,2,1,1,1] => 5268509 [5,2,1,1,1,1,1] => 2324232 [5,1,1,1,1,1,1,1] => 411617 [4,4,4] => 767374 [4,4,3,1] => 4672515 [4,4,2,2] => 4046784 [4,4,2,1,1] => 6654415 [4,4,1,1,1,1] => 2736039 [4,3,3,2] => 4431193 [4,3,3,1,1] => 6048237 [4,3,2,2,1] => 8196079 [4,3,2,1,1,1] => 7708135 [4,3,1,1,1,1,1] => 2687248 [4,2,2,2,2] => 2007817 [4,2,2,2,1,1] => 4067001 [4,2,2,1,1,1,1] => 2999761 [4,2,1,1,1,1,1,1] => 1120777 [4,1,1,1,1,1,1,1,1] => 181323 [3,3,3,3] => 653476 [3,3,3,2,1] => 2880740 [3,3,3,1,1,1] => 2172252 [3,3,2,2,2] => 1737900 [3,3,2,2,1,1] => 3438253 [3,3,2,1,1,1,1] => 2368802 [3,3,1,1,1,1,1,1] => 712438 [3,2,2,2,2,1] => 1419280 [3,2,2,2,1,1,1] => 1674954 [3,2,2,1,1,1,1,1] => 1007873 [3,2,1,1,1,1,1,1,1] => 339353 [3,1,1,1,1,1,1,1,1,1] => 54170 [2,2,2,2,2,2] => 151661 [2,2,2,2,2,1,1] => 334219 [2,2,2,2,1,1,1,1] => 297635 [2,2,2,1,1,1,1,1,1] => 158017 [2,2,1,1,1,1,1,1,1,1] => 51998 [2,1,1,1,1,1,1,1,1,1,1] => 9899 [1,1,1,1,1,1,1,1,1,1,1,1] => 841 [13] => 12486 [12,1] => 117560 [11,2] => 526938 [11,1,1] => 517187 [10,3] => 1454530 [10,2,1] => 2863468 [10,1,1,1] => 1402768 [9,4] => 2684621 [9,3,1] => 8049646 [9,2,2] => 5365056 [9,2,1,1] => 7963420 [9,1,1,1,1] => 2608389 [8,5] => 3312394 [8,4,1] => 13866810 [8,3,2] => 17733622 [8,3,1,1] => 21172350 [8,2,2,1] => 17818309 [8,2,1,1,1] => 14128937 [8,1,1,1,1,1] => 3499254 [7,6] => 2373015 [7,5,1] => 14521026 [7,4,2] => 28864981 [7,4,1,1] => 32116116 [7,3,3] => 16723498 [7,3,2,1] => 54036226 [7,3,1,1,1] => 33770537 [7,2,2,2] => 17340374 [7,2,2,1,1] => 31128235 [7,2,1,1,1,1] => 17260955 [7,1,1,1,1,1,1] => 3470680 [6,6,1] => 6345797 [6,5,2] => 23702675 [6,5,1,1] => 25650810 [6,4,3] => 28460048 [6,4,2,1] => 73035793 [6,4,1,1,1] => 42208136 [6,3,3,1] => 47451871 [6,3,2,2] => 48616209 [6,3,2,1,1] => 81330806 [6,3,1,1,1,1] => 35264276 [6,2,2,2,1] => 34329413 [6,2,2,1,1,1] => 34445325 [6,2,1,1,1,1,1] => 14937254 [6,1,1,1,1,1,1,1] => 2563710 [5,5,3] => 14762478 [5,5,2,1] => 35529815 [5,5,1,1,1] => 19970378 [5,4,4] => 10782449 [5,4,3,1] => 59818074 [5,4,2,2] => 50043270 [5,4,2,1,1] => 81423905 [5,4,1,1,1,1] => 32643245 [5,3,3,2] => 43925679 [5,3,3,1,1] => 59317092 [5,3,2,2,1] => 77619191 [5,3,2,1,1,1] => 72016943 [5,3,1,1,1,1,1] => 24414568 [5,2,2,2,2] => 17300648 [5,2,2,2,1,1] => 34807415 [5,2,2,1,1,1,1] => 25266951 [5,2,1,1,1,1,1,1] => 9156430 [5,1,1,1,1,1,1,1,1] => 1399954 [4,4,4,1] => 13149059 [4,4,3,2] => 31702900 [4,4,3,1,1] => 41807708 [4,4,2,2,1] => 45394673 [4,4,2,1,1,1] => 40962030 [4,4,1,1,1,1,1] => 12937775 [4,3,3,3] => 12227135 [4,3,3,2,1] => 51699039 [4,3,3,1,1,1] => 38100605 [4,3,2,2,2] => 28570505 [4,3,2,2,1,1] => 55907499 [4,3,2,1,1,1,1] => 37522830 [4,3,1,1,1,1,1,1] => 10710735 [4,2,2,2,2,1] => 17843375 [4,2,2,2,1,1,1] => 20762403 [4,2,2,1,1,1,1,1] => 12134332 [4,2,1,1,1,1,1,1,1] => 3865062 [4,1,1,1,1,1,1,1,1,1] => 551430 [3,3,3,3,1] => 8450034 [3,3,3,2,2] => 11024598 [3,3,3,2,1,1] => 20234283 [3,3,3,1,1,1,1] => 10785694 [3,3,2,2,2,1] => 15681116 [3,3,2,2,1,1,1] => 17746031 [3,3,2,1,1,1,1,1] => 9662228 [3,3,1,1,1,1,1,1,1] => 2473578 [3,2,2,2,2,2] => 3721471 [3,2,2,2,2,1,1] => 8108579 [3,2,2,2,1,1,1,1] => 7028312 [3,2,2,1,1,1,1,1,1] => 3535088 [3,2,1,1,1,1,1,1,1,1] => 1041251 [3,1,1,1,1,1,1,1,1,1,1] => 148892 [2,2,2,2,2,2,1] => 1144504 [2,2,2,2,2,1,1,1] => 1485062 [2,2,2,2,1,1,1,1,1] => 1067450 [2,2,2,1,1,1,1,1,1,1] => 489921 [2,2,1,1,1,1,1,1,1,1,1] => 143725 [2,1,1,1,1,1,1,1,1,1,1,1] => 24803 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 1937 [14] => 32973 [13,1] => 337830 [12,2] => 1654257 [12,1,1] => 1624554 [11,3] => 5039926 [11,2,1] => 9902842 [11,1,1,1] => 4847734 [10,4] => 10456926 [10,3,1] => 31108545 [10,2,2] => 20654979 [10,2,1,1] => 30628756 [10,1,1,1,1] => 10003154 [9,5] => 15077304 [9,4,1] => 61538238 [9,3,2] => 77693810 [9,3,1,1] => 92557381 [9,2,2,1] => 77386723 [9,2,1,1,1] => 61186563 [9,1,1,1,1,1] => 15059202 [8,6] => 14249222 [8,5,1] => 78994961 [8,4,2] => 150135855 [8,4,1,1] => 166414274 [8,3,3] => 85407750 [8,3,2,1] => 273766926 [8,3,1,1,1] => 170241639 [8,2,2,2] => 86678879 [8,2,2,1,1] => 155210847 [8,2,1,1,1,1] => 85547356 [8,1,1,1,1,1,1] => 17006324 [7,7] => 5938318 [7,6,1] => 57783051 [7,5,2] => 166091679 [7,5,1,1] => 178617975 [7,4,3] => 182865109 [7,4,2,1] => 463145636 [7,4,1,1,1] => 265495761 [7,3,3,1] => 290670069 [7,3,2,2] => 294560241 [7,3,2,1,1] => 490735466 [7,3,1,1,1,1] => 210742474 [7,2,2,2,1] => 202418417 [7,2,2,1,1,1] => 201992533 [7,2,1,1,1,1,1] => 86634985 [7,1,1,1,1,1,1,1] => 14582319 [6,6,2] => 74283437 [6,6,1,1] => 78949145 [6,5,3] => 164915955 [6,5,2,1] => 388110594 [6,5,1,1,1] => 215279308 [6,4,4] => 96548839 [6,4,3,1] => 511886812 [6,4,2,2] => 420309243 [6,4,2,1,1] => 679358312 [6,4,1,1,1,1] => 268205412 [6,3,3,2] => 342184157 [6,3,3,1,1] => 458988254 [6,3,2,2,1] => 589362757 [6,3,2,1,1,1] => 542133855 [6,3,1,1,1,1,1] => 180657554 [6,2,2,2,2] => 125420661 [6,2,2,2,1,1] => 251217686 [6,2,2,1,1,1,1] => 180494649 [6,2,1,1,1,1,1,1] => 64181517 [6,1,1,1,1,1,1,1,1] => 9493753 [5,5,4] => 62758253 [5,5,3,1] => 269611885 [5,5,2,2] => 209195646 [5,5,2,1,1] => 334158123 [5,5,1,1,1,1] => 127982874 [5,4,4,1] => 204763407 [5,4,3,2] => 452456209 [5,4,3,1,1] => 590211424 [5,4,2,2,1] => 618787954 [5,4,2,1,1,1] => 550754654 [5,4,1,1,1,1,1] => 169152560 [5,3,3,3] => 136666196 [5,3,3,2,1] => 564685782 [5,3,3,1,1,1] => 410439810 [5,3,2,2,2] => 299194543 [5,3,2,2,1,1] => 581416259 [5,3,2,1,1,1,1] => 384016010 [5,3,1,1,1,1,1,1] => 106357366 [5,2,2,2,2,1] => 168752177 [5,2,2,2,1,1,1] => 194582233 [5,2,2,1,1,1,1,1] => 111684023 [5,2,1,1,1,1,1,1,1] => 34441448 [5,1,1,1,1,1,1,1,1,1] => 4636148 [4,4,4,2] => 109175788 [4,4,4,1,1] => 133555377 [4,4,3,3] => 106773534 [4,4,3,2,1] => 413699745 [4,4,3,1,1,1] => 292419408 [4,4,2,2,2] => 178971175 [4,4,2,2,1,1] => 343701813 [4,4,2,1,1,1,1] => 220223262 [4,4,1,1,1,1,1,1] => 56731883 [4,3,3,3,1] => 175138306 [4,3,3,2,2] => 220601134 [4,3,3,2,1,1] => 400371062 [4,3,3,1,1,1,1] => 207879257 [4,3,2,2,2,1] => 284131158 [4,3,2,2,1,1,1] => 317001906 [4,3,2,1,1,1,1,1] => 167689187 [4,3,1,1,1,1,1,1,1] => 40646984 [4,2,2,2,2,2] => 51754089 [4,2,2,2,2,1,1] => 111953052 [4,2,2,2,1,1,1,1] => 95426777 [4,2,2,1,1,1,1,1,1] => 46517150 [4,2,1,1,1,1,1,1,1,1] => 12937639 [4,1,1,1,1,1,1,1,1,1,1] => 1651612 [3,3,3,3,2] => 46932665 [3,3,3,3,1,1] => 69026719 [3,3,3,2,2,1] => 112807355 [3,3,3,2,1,1,1] => 116948640 [3,3,3,1,1,1,1,1] => 48874832 [3,3,2,2,2,2] => 46507230 [3,3,2,2,2,1,1] => 99421226 [3,3,2,2,1,1,1,1] => 82211205 [3,3,2,1,1,1,1,1,1] => 37274049 [3,3,1,1,1,1,1,1,1,1] => 8322668 [3,2,2,2,2,2,1] => 30960925 [3,2,2,2,2,1,1,1] => 39587695 [3,2,2,2,1,1,1,1,1] => 27617045 [3,2,2,1,1,1,1,1,1,1] => 11982968 [3,2,1,1,1,1,1,1,1,1,1] => 3140626 [3,1,1,1,1,1,1,1,1,1,1,1] => 406926 [2,2,2,2,2,2,2] => 2719750 [2,2,2,2,2,2,1,1] => 6240983 [2,2,2,2,2,1,1,1,1] => 6043832 [2,2,2,2,1,1,1,1,1,1] => 3675528 [2,2,2,1,1,1,1,1,1,1,1] => 1489539 [2,2,1,1,1,1,1,1,1,1,1,1] => 394399 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 62277 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 4488 [15] => 87811 [14,1] => 972027 [13,2] => 5162510 [13,1,1] => 5072470 [12,3] => 17194564 [12,2,1] => 33749476 [12,1,1,1] => 16517440 [11,4] => 39536708 [11,3,1] => 117034850 [11,2,2] => 77519018 [11,2,1,1] => 114886192 [11,1,1,1,1] => 37456239 [10,5] => 64818488 [10,4,1] => 260559486 [10,3,2] => 326328078 [10,3,1,1] => 388214926 [10,2,2,1] => 323217583 [10,2,1,1,1] => 255082332 [10,1,1,1,1,1] => 62526377 [9,6] => 74188203 [9,5,1] => 391657956 [9,4,2] => 725990084 [9,4,1,1] => 802704875 [9,3,3] => 408562603 [9,3,2,1] => 1302839869 [9,3,1,1,1] => 807510347 [9,2,2,2] => 409009574 [9,2,2,1,1] => 731162883 [9,2,1,1,1,1] => 401385752 [9,1,1,1,1,1,1] => 79195818 [8,7] => 50965136 [8,6,1] => 379122068 [8,5,2] => 988331785 [8,5,1,1] => 1058562658 [8,4,3] => 1043986974 [8,4,1,1,1] => 1495221953 [8,3,3,1] => 1615236170 [8,3,2,2] => 1625643526 [8,3,1,1,1,1] => 1152516097 [8,2,2,2,1] => 1098655937 [8,2,2,1,1,1] => 1092312951 [8,2,1,1,1,1,1] => 465080787 [8,1,1,1,1,1,1,1] => 77293835 [7,7,1] => 159750388 [7,6,2] => 744172569 [7,6,1,1] => 785771135 [7,5,3] => 1278904432 [7,5,1,1,1] => 1633379117 [7,4,4] => 694421799 [7,4,1,1,1,1] => 1833656854 [7,3,1,1,1,1,1] => 1171129666 [7,2,2,2,2] => 805562674 [7,2,2,2,1,1] => 1608676864 [7,2,2,1,1,1,1] => 1147891361 [7,2,1,1,1,1,1,1] => 403148722 [7,1,1,1,1,1,1,1,1] => 58405033 [6,6,3] => 594561395 [6,6,2,1] => 1342465290 [6,6,1,1,1] => 727953397 [6,5,4] => 804252594 [6,5,1,1,1,1] => 1503500213 [6,4,4,1] => 2008573926 [6,4,1,1,1,1,1] => 1510677178 [6,3,3,3] => 1177946350 [6,3,1,1,1,1,1,1] => 853700235 [6,2,2,2,2,1] => 1331035536 [6,2,2,2,1,1,1] => 1525453458 [6,2,2,1,1,1,1,1] => 865269336 [6,2,1,1,1,1,1,1,1] => 261447141 [6,1,1,1,1,1,1,1,1,1] => 34004305 [5,5,5] => 155371996 [5,5,4,1] => 1325076561 [5,5,1,1,1,1,1] => 725509751 [5,4,4,2] => 1884385521 [5,4,3,3] => 1708792896 [5,4,1,1,1,1,1,1] => 806327926 [5,3,3,3,1] => 2143806319 [5,3,2,1,1,1,1,1] => 1864999798 [5,3,1,1,1,1,1,1,1] => 437864205 [5,2,2,2,2,2] => 535343174 [5,2,2,2,2,1,1] => 1152435786 [5,2,2,2,1,1,1,1] => 971636938 [5,2,2,1,1,1,1,1,1] => 464388438 [5,2,1,1,1,1,1,1,1,1] => 124863051 [5,1,1,1,1,1,1,1,1,1,1] => 15020917 [4,4,4,3] => 529303489 [4,4,4,2,1] => 1605699258 [4,4,4,1,1,1] => 1039872691 [4,4,3,3,1] => 1699418976 [4,4,3,2,2] => 1984352702 [4,4,3,1,1,1,1] => 1751211917 [4,4,2,2,2,1] => 1962392850 [4,4,2,2,1,1,1] => 2138583579 [4,4,2,1,1,1,1,1] => 1076174044 [4,4,1,1,1,1,1,1,1] => 234751233 [4,3,3,3,2] => 1078157705 [4,3,3,3,1,1] => 1567775172 [4,3,3,1,1,1,1,1] => 1026160738 [4,3,2,2,2,2] => 926836436 [4,3,2,2,2,1,1] => 1966898497 [4,3,2,2,1,1,1,1] => 1599536383 [4,3,2,1,1,1,1,1,1] => 703125821 [4,3,1,1,1,1,1,1,1,1] => 148387203 [4,2,2,2,2,2,1] => 469936718 [4,2,2,2,2,1,1,1] => 595145513 [4,2,2,2,1,1,1,1,1] => 407483258 [4,2,2,1,1,1,1,1,1,1] => 171059312 [4,2,1,1,1,1,1,1,1,1,1] => 42274159 [4,1,1,1,1,1,1,1,1,1,1,1] => 4884926 [3,3,3,3,3] => 113973816 [3,3,3,3,2,1] => 554525027 [3,3,3,3,1,1,1] => 449972148 [3,3,3,2,2,2] => 385501205 [3,3,3,2,2,1,1] => 795561721 [3,3,3,2,1,1,1,1] => 598052628 [3,3,3,1,1,1,1,1,1] => 207033802 [3,3,2,2,2,2,1] => 426563586 [3,3,2,2,2,1,1,1] => 532543453 [3,3,2,2,1,1,1,1,1] => 353150826 [3,3,2,1,1,1,1,1,1,1] => 137739677 [3,3,1,1,1,1,1,1,1,1,1] => 27305619 [3,2,2,2,2,2,2] => 80958568 [3,2,2,2,2,2,1,1] => 184371259 [3,2,2,2,2,1,1,1,1] => 175492754 [3,2,2,2,1,1,1,1,1,1] => 103369125 [3,2,2,1,1,1,1,1,1,1,1] => 39535615 [3,2,1,1,1,1,1,1,1,1,1,1] => 9341114 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 1106787 [2,2,2,2,2,2,2,1] => 21438058 [2,2,2,2,2,2,1,1,1] => 29344677 [2,2,2,2,2,1,1,1,1,1] => 23159883 [2,2,2,2,1,1,1,1,1,1,1] => 12268309 [2,2,2,1,1,1,1,1,1,1,1,1] => 4458118 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 1076106 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 156635 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 10470 [16] => 235381 [15,1] => 2800210 [14,2] => 16030711 [14,1,1] => 15760718 [13,3] => 57922032 [13,2,1] => 113629123 [13,1,1,1] => 55614698 [12,4] => 145993458 [12,3,1] => 430796257 [12,2,2] => 284890592 [12,2,1,1] => 422103925 [12,1,1,1,1] => 137481101 [11,5] => 267178895 [11,4,1] => 1063722818 [11,3,2] => 1325271009 [11,3,1,1] => 1575196622 [11,2,2,1] => 1307806764 [11,2,1,1,1] => 1030906484 [11,1,1,1,1,1] => 252034735 [10,6] => 354580296 [10,5,1] => 1820774416 [10,3,3] => 1858162722 [10,2,2,2] => 1843448903 [10,2,1,1,1,1] => 1802234216 [10,1,1,1,1,1,1] => 353805825 [9,7] => 318473957 [9,6,1] => 2139325004 [9,1,1,1,1,1,1,1] => 387162287 [8,8] => 129535248 [8,7,1] => 1490784962 [8,1,1,1,1,1,1,1,1] => 332915234 [7,2,1,1,1,1,1,1,1] => 1767866133 [7,1,1,1,1,1,1,1,1,1] => 224946705 [6,2,1,1,1,1,1,1,1,1] => 1020358944 [6,1,1,1,1,1,1,1,1,1,1] => 118477879 [5,3,1,1,1,1,1,1,1,1] => 1723206656 [5,2,2,1,1,1,1,1,1,1] => 1840737571 [5,2,1,1,1,1,1,1,1,1,1] => 439255517 [5,1,1,1,1,1,1,1,1,1,1,1] => 47785430 [4,4,4,4] => 1306046046 [4,4,1,1,1,1,1,1,1,1] => 927611299 [4,3,1,1,1,1,1,1,1,1,1] => 524922173 [4,2,2,2,2,2,2] => 1337861000 [4,2,2,2,1,1,1,1,1,1] => 1646507663 [4,2,2,1,1,1,1,1,1,1,1] => 608446614 [4,2,1,1,1,1,1,1,1,1,1,1] => 135403979 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 14295748 [3,3,3,3,3,1] => 1631749681 [3,3,3,1,1,1,1,1,1,1] => 832477037 [3,3,2,2,2,2,2] => 1231379074 [3,3,2,2,1,1,1,1,1,1] => 1433601427 [3,3,2,1,1,1,1,1,1,1,1] => 491833726 [3,3,1,1,1,1,1,1,1,1,1,1] => 87751048 [3,2,2,2,2,2,2,1] => 693138608 [3,2,2,2,2,2,1,1,1] => 939406998 [3,2,2,2,2,1,1,1,1,1] => 727322272 [3,2,2,2,1,1,1,1,1,1,1] => 372574501 [3,2,2,1,1,1,1,1,1,1,1,1] => 127604626 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 27461558 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2997745 [2,2,2,2,2,2,2,2] => 51631096 [2,2,2,2,2,2,2,1,1] => 122192606 [2,2,2,2,2,2,1,1,1,1] => 126113655 [2,2,2,2,2,1,1,1,1,1,1] => 84885341 [2,2,2,2,1,1,1,1,1,1,1,1] => 39952525 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 13172019 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 2922614 [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 394541 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 24617 [17] => 634847 [16,1] => 8075889 [15,2] => 49573027 [15,1,1] => 48766303 [14,3] => 193057849 [14,2,1] => 378664173 [14,1,1,1] => 185378712 [13,4] => 528810821 [13,3,1] => 1557249811 [13,2,2] => 1028777845 [13,2,1,1] => 1524130518 [13,1,1,1,1] => 496169063 [12,5] => 1065941036 [12,1,1,1,1,1] => 990929161 [11,6] => 1597860048 [11,1,1,1,1,1,1] => 1526944296 [10,7] => 1725014317 [10,1,1,1,1,1,1,1] => 1851293429 [9,8] => 1146402753 [9,1,1,1,1,1,1,1,1] => 1784473033 [8,1,1,1,1,1,1,1,1,1] => 1371962305 [7,1,1,1,1,1,1,1,1,1,1] => 838596407 [6,1,1,1,1,1,1,1,1,1,1,1] => 403313023 [5,2,1,1,1,1,1,1,1,1,1,1] => 1507004012 [5,1,1,1,1,1,1,1,1,1,1,1,1] => 149673796 [4,3,1,1,1,1,1,1,1,1,1,1] => 1809106792 [4,2,2,1,1,1,1,1,1,1,1,1] => 2105875810 [4,2,1,1,1,1,1,1,1,1,1,1,1] => 426488173 [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 41459188 [3,3,2,1,1,1,1,1,1,1,1,1] => 1707635704 [3,3,1,1,1,1,1,1,1,1,1,1,1] => 277153166 [3,2,2,2,2,2,2,2] => 1810230869 [3,2,2,2,1,1,1,1,1,1,1,1] => 1302782039 [3,2,2,1,1,1,1,1,1,1,1,1,1] => 404412154 ----------------------------------------------------------------------------- Created: Sep 26, 2020 at 23:49 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 26, 2020 at 23:49 by Martin Rubey