***************************************************************************** * 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: St001936 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of transitive factorisations of a permutation of given cycle type into star transpositions. Let $\pi$ be a permutation of cycle type $\lambda\vdash n$ and let $r=n + \ell(\lambda) - 2$. A minimal factorization of $\pi$ into star transpositions is an $r$-tuple of transpositions $(1, a_1)\dots(1, a_r)$ whose product (in this order) equals $\pi$. The number of such factorizations equals [1] $$ \frac{r!}{n!} \lambda_1\dots\lambda_{\ell(\lambda)}. $$ ----------------------------------------------------------------------------- References: [1] Irving, J., Rattan, A. Minimal factorizations of permutations into star transpositions [[MathSciNet:2510551]] ----------------------------------------------------------------------------- Code: def statistic(la): n = la.size() r = n + len(la) - 2 return factorial(r) / factorial(n) * prod(p for p in la) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 1 [1,1] => 1 [3] => 1 [2,1] => 2 [1,1,1] => 4 [4] => 1 [3,1] => 3 [2,2] => 4 [2,1,1] => 10 [1,1,1,1] => 30 [5] => 1 [4,1] => 4 [3,2] => 6 [3,1,1] => 18 [2,2,1] => 24 [2,1,1,1] => 84 [1,1,1,1,1] => 336 [6] => 1 [5,1] => 5 [4,2] => 8 [4,1,1] => 28 [3,3] => 9 [3,2,1] => 42 [3,1,1,1] => 168 [2,2,2] => 56 [2,2,1,1] => 224 [2,1,1,1,1] => 1008 [1,1,1,1,1,1] => 5040 [7] => 1 [6,1] => 6 [5,2] => 10 [5,1,1] => 40 [4,3] => 12 [4,2,1] => 64 [4,1,1,1] => 288 [3,3,1] => 72 [3,2,2] => 96 [3,2,1,1] => 432 [3,1,1,1,1] => 2160 [2,2,2,1] => 576 [2,2,1,1,1] => 2880 [2,1,1,1,1,1] => 15840 [1,1,1,1,1,1,1] => 95040 [8] => 1 [7,1] => 7 [6,2] => 12 [6,1,1] => 54 [5,3] => 15 [5,2,1] => 90 [5,1,1,1] => 450 [4,4] => 16 [4,3,1] => 108 [4,2,2] => 144 [4,2,1,1] => 720 [4,1,1,1,1] => 3960 [3,3,2] => 162 [3,3,1,1] => 810 [3,2,2,1] => 1080 [3,2,1,1,1] => 5940 [3,1,1,1,1,1] => 35640 [2,2,2,2] => 1440 [2,2,2,1,1] => 7920 [2,2,1,1,1,1] => 47520 [2,1,1,1,1,1,1] => 308880 [1,1,1,1,1,1,1,1] => 2162160 [9] => 1 [8,1] => 8 [7,2] => 14 [7,1,1] => 70 [6,3] => 18 [6,2,1] => 120 [6,1,1,1] => 660 [5,4] => 20 [5,3,1] => 150 [5,2,2] => 200 [5,2,1,1] => 1100 [5,1,1,1,1] => 6600 [4,4,1] => 160 [4,3,2] => 240 [4,3,1,1] => 1320 [4,2,2,1] => 1760 [4,2,1,1,1] => 10560 [4,1,1,1,1,1] => 68640 [3,3,3] => 270 [3,3,2,1] => 1980 [3,3,1,1,1] => 11880 [3,2,2,2] => 2640 [3,2,2,1,1] => 15840 [3,2,1,1,1,1] => 102960 [3,1,1,1,1,1,1] => 720720 [2,2,2,2,1] => 21120 [2,2,2,1,1,1] => 137280 [2,2,1,1,1,1,1] => 960960 [2,1,1,1,1,1,1,1] => 7207200 [1,1,1,1,1,1,1,1,1] => 57657600 [10] => 1 [9,1] => 9 [8,2] => 16 [8,1,1] => 88 [7,3] => 21 [7,2,1] => 154 [7,1,1,1] => 924 [6,4] => 24 [6,3,1] => 198 [6,2,2] => 264 [6,2,1,1] => 1584 [6,1,1,1,1] => 10296 [5,5] => 25 [5,4,1] => 220 [5,3,2] => 330 [5,3,1,1] => 1980 [5,2,2,1] => 2640 [5,2,1,1,1] => 17160 [5,1,1,1,1,1] => 120120 [4,4,2] => 352 [4,4,1,1] => 2112 [4,3,3] => 396 [4,3,2,1] => 3168 [4,3,1,1,1] => 20592 [4,2,2,2] => 4224 [4,2,2,1,1] => 27456 [4,2,1,1,1,1] => 192192 [4,1,1,1,1,1,1] => 1441440 [3,3,3,1] => 3564 [3,3,2,2] => 4752 [3,3,2,1,1] => 30888 [3,3,1,1,1,1] => 216216 [3,2,2,2,1] => 41184 [3,2,2,1,1,1] => 288288 [3,2,1,1,1,1,1] => 2162160 [3,1,1,1,1,1,1,1] => 17297280 [2,2,2,2,2] => 54912 [2,2,2,2,1,1] => 384384 [2,2,2,1,1,1,1] => 2882880 [2,2,1,1,1,1,1,1] => 23063040 [2,1,1,1,1,1,1,1,1] => 196035840 [1,1,1,1,1,1,1,1,1,1] => 1764322560 [11] => 1 [10,1] => 10 [9,2] => 18 [9,1,1] => 108 [8,3] => 24 [8,2,1] => 192 [8,1,1,1] => 1248 [7,4] => 28 [7,3,1] => 252 [7,2,2] => 336 [7,2,1,1] => 2184 [7,1,1,1,1] => 15288 [6,5] => 30 [6,4,1] => 288 [6,3,2] => 432 [6,3,1,1] => 2808 [6,2,2,1] => 3744 [6,2,1,1,1] => 26208 [6,1,1,1,1,1] => 196560 [5,5,1] => 300 [5,4,2] => 480 [5,4,1,1] => 3120 [5,3,3] => 540 [5,3,2,1] => 4680 [5,3,1,1,1] => 32760 [5,2,2,2] => 6240 [5,2,2,1,1] => 43680 [5,2,1,1,1,1] => 327600 [5,1,1,1,1,1,1] => 2620800 [4,4,3] => 576 [4,4,2,1] => 4992 [4,4,1,1,1] => 34944 [4,3,3,1] => 5616 [4,3,2,2] => 7488 [4,3,2,1,1] => 52416 [4,3,1,1,1,1] => 393120 [4,2,2,2,1] => 69888 [4,2,2,1,1,1] => 524160 [4,2,1,1,1,1,1] => 4193280 [4,1,1,1,1,1,1,1] => 35642880 [3,3,3,2] => 8424 [3,3,3,1,1] => 58968 [3,3,2,2,1] => 78624 [3,3,2,1,1,1] => 589680 [3,3,1,1,1,1,1] => 4717440 [3,2,2,2,2] => 104832 [3,2,2,2,1,1] => 786240 [3,2,2,1,1,1,1] => 6289920 [3,2,1,1,1,1,1,1] => 53464320 [3,1,1,1,1,1,1,1,1] => 481178880 [2,2,2,2,2,1] => 1048320 [2,2,2,2,1,1,1] => 8386560 [2,2,2,1,1,1,1,1] => 71285760 [2,2,1,1,1,1,1,1,1] => 641571840 [12] => 1 [11,1] => 11 [10,2] => 20 [10,1,1] => 130 [9,3] => 27 [9,2,1] => 234 [9,1,1,1] => 1638 [8,4] => 32 [8,3,1] => 312 [8,2,2] => 416 [8,2,1,1] => 2912 [8,1,1,1,1] => 21840 [7,5] => 35 [7,4,1] => 364 [7,3,2] => 546 [7,3,1,1] => 3822 [7,2,2,1] => 5096 [7,2,1,1,1] => 38220 [7,1,1,1,1,1] => 305760 [6,6] => 36 [6,5,1] => 390 [6,4,2] => 624 [6,4,1,1] => 4368 [6,3,3] => 702 [6,3,2,1] => 6552 [6,3,1,1,1] => 49140 [6,2,2,2] => 8736 [6,2,2,1,1] => 65520 [6,2,1,1,1,1] => 524160 [6,1,1,1,1,1,1] => 4455360 [5,5,2] => 650 [5,5,1,1] => 4550 [5,4,3] => 780 [5,4,2,1] => 7280 [5,4,1,1,1] => 54600 [5,3,3,1] => 8190 [5,3,2,2] => 10920 [5,3,2,1,1] => 81900 [5,3,1,1,1,1] => 655200 [5,2,2,2,1] => 109200 [5,2,2,1,1,1] => 873600 [5,2,1,1,1,1,1] => 7425600 [5,1,1,1,1,1,1,1] => 66830400 [4,4,4] => 832 [4,4,3,1] => 8736 [4,4,2,2] => 11648 [4,4,2,1,1] => 87360 [4,4,1,1,1,1] => 698880 [4,3,3,2] => 13104 [4,3,3,1,1] => 98280 [4,3,2,2,1] => 131040 [4,3,2,1,1,1] => 1048320 [4,3,1,1,1,1,1] => 8910720 [4,2,2,2,2] => 174720 [4,2,2,2,1,1] => 1397760 [4,2,2,1,1,1,1] => 11880960 [4,2,1,1,1,1,1,1] => 106928640 [4,1,1,1,1,1,1,1,1] => 1015822080 [3,3,3,3] => 14742 [3,3,3,2,1] => 147420 [3,3,3,1,1,1] => 1179360 [3,3,2,2,2] => 196560 [3,3,2,2,1,1] => 1572480 [3,3,2,1,1,1,1] => 13366080 [3,3,1,1,1,1,1,1] => 120294720 [3,2,2,2,2,1] => 2096640 [3,2,2,2,1,1,1] => 17821440 [3,2,2,1,1,1,1,1] => 160392960 [3,2,1,1,1,1,1,1,1] => 1523733120 [2,2,2,2,2,2] => 2795520 [2,2,2,2,2,1,1] => 23761920 [2,2,2,2,1,1,1,1] => 213857280 [2,2,2,1,1,1,1,1,1] => 2031644160 [13] => 1 [12,1] => 12 [11,2] => 22 [11,1,1] => 154 [10,3] => 30 [10,2,1] => 280 [10,1,1,1] => 2100 [9,4] => 36 [9,3,1] => 378 [9,2,2] => 504 [9,2,1,1] => 3780 [9,1,1,1,1] => 30240 [8,5] => 40 [8,4,1] => 448 [8,3,2] => 672 [8,3,1,1] => 5040 [8,2,2,1] => 6720 [8,2,1,1,1] => 53760 [8,1,1,1,1,1] => 456960 [7,6] => 42 [7,5,1] => 490 [7,4,2] => 784 [7,4,1,1] => 5880 [7,3,3] => 882 [7,3,2,1] => 8820 [7,3,1,1,1] => 70560 [7,2,2,2] => 11760 [7,2,2,1,1] => 94080 [7,2,1,1,1,1] => 799680 [7,1,1,1,1,1,1] => 7197120 [6,6,1] => 504 [6,5,2] => 840 [6,5,1,1] => 6300 [6,4,3] => 1008 [6,4,2,1] => 10080 [6,4,1,1,1] => 80640 [6,3,3,1] => 11340 [6,3,2,2] => 15120 [6,3,2,1,1] => 120960 [6,3,1,1,1,1] => 1028160 [6,2,2,2,1] => 161280 [6,2,2,1,1,1] => 1370880 [6,2,1,1,1,1,1] => 12337920 [6,1,1,1,1,1,1,1] => 117210240 [5,5,3] => 1050 [5,5,2,1] => 10500 [5,5,1,1,1] => 84000 [5,4,4] => 1120 [5,4,3,1] => 12600 [5,4,2,2] => 16800 [5,4,2,1,1] => 134400 [5,4,1,1,1,1] => 1142400 [5,3,3,2] => 18900 [5,3,3,1,1] => 151200 [5,3,2,2,1] => 201600 [5,3,2,1,1,1] => 1713600 [5,3,1,1,1,1,1] => 15422400 [5,2,2,2,2] => 268800 [5,2,2,2,1,1] => 2284800 [5,2,2,1,1,1,1] => 20563200 [5,2,1,1,1,1,1,1] => 195350400 [5,1,1,1,1,1,1,1,1] => 1953504000 [4,4,4,1] => 13440 [4,4,3,2] => 20160 [4,4,3,1,1] => 161280 [4,4,2,2,1] => 215040 [4,4,2,1,1,1] => 1827840 [4,4,1,1,1,1,1] => 16450560 [4,3,3,3] => 22680 [4,3,3,2,1] => 241920 [4,3,3,1,1,1] => 2056320 [4,3,2,2,2] => 322560 [4,3,2,2,1,1] => 2741760 [4,3,2,1,1,1,1] => 24675840 [4,3,1,1,1,1,1,1] => 234420480 [4,2,2,2,2,1] => 3655680 [4,2,2,2,1,1,1] => 32901120 [4,2,2,1,1,1,1,1] => 312560640 [3,3,3,3,1] => 272160 [3,3,3,2,2] => 362880 [3,3,3,2,1,1] => 3084480 [3,3,3,1,1,1,1] => 27760320 [3,3,2,2,2,1] => 4112640 [3,3,2,2,1,1,1] => 37013760 [3,3,2,1,1,1,1,1] => 351630720 [3,2,2,2,2,2] => 5483520 [3,2,2,2,2,1,1] => 49351680 [3,2,2,2,1,1,1,1] => 468840960 [2,2,2,2,2,2,1] => 65802240 [2,2,2,2,2,1,1,1] => 625121280 [14] => 1 [13,1] => 13 [12,2] => 24 [12,1,1] => 180 [11,3] => 33 [11,2,1] => 330 [11,1,1,1] => 2640 [10,4] => 40 [10,3,1] => 450 [10,2,2] => 600 [10,2,1,1] => 4800 [10,1,1,1,1] => 40800 [9,5] => 45 [9,4,1] => 540 [9,3,2] => 810 [9,3,1,1] => 6480 [9,2,2,1] => 8640 [9,2,1,1,1] => 73440 [9,1,1,1,1,1] => 660960 [8,6] => 48 [8,5,1] => 600 [8,4,2] => 960 [8,4,1,1] => 7680 [8,3,3] => 1080 [8,3,2,1] => 11520 [8,3,1,1,1] => 97920 [8,2,2,2] => 15360 [8,2,2,1,1] => 130560 [8,2,1,1,1,1] => 1175040 [8,1,1,1,1,1,1] => 11162880 [7,7] => 49 [7,6,1] => 630 [7,5,2] => 1050 [7,5,1,1] => 8400 [7,4,3] => 1260 [7,4,2,1] => 13440 [7,4,1,1,1] => 114240 [7,3,3,1] => 15120 [7,3,2,2] => 20160 [7,3,2,1,1] => 171360 [7,3,1,1,1,1] => 1542240 [7,2,2,2,1] => 228480 [7,2,2,1,1,1] => 2056320 [7,2,1,1,1,1,1] => 19535040 [7,1,1,1,1,1,1,1] => 195350400 [6,6,2] => 1080 [6,6,1,1] => 8640 [6,5,3] => 1350 [6,5,2,1] => 14400 [6,5,1,1,1] => 122400 [6,4,4] => 1440 [6,4,3,1] => 17280 [6,4,2,2] => 23040 [6,4,2,1,1] => 195840 [6,4,1,1,1,1] => 1762560 [6,3,3,2] => 25920 [6,3,3,1,1] => 220320 [6,3,2,2,1] => 293760 [6,3,2,1,1,1] => 2643840 [6,3,1,1,1,1,1] => 25116480 [6,2,2,2,2] => 391680 [6,2,2,2,1,1] => 3525120 [6,2,2,1,1,1,1] => 33488640 [6,2,1,1,1,1,1,1] => 334886400 [5,5,4] => 1500 [5,5,3,1] => 18000 [5,5,2,2] => 24000 [5,5,2,1,1] => 204000 [5,5,1,1,1,1] => 1836000 [5,4,4,1] => 19200 [5,4,3,2] => 28800 [5,4,3,1,1] => 244800 [5,4,2,2,1] => 326400 [5,4,2,1,1,1] => 2937600 [5,4,1,1,1,1,1] => 27907200 [5,3,3,3] => 32400 [5,3,3,2,1] => 367200 [5,3,3,1,1,1] => 3304800 [5,3,2,2,2] => 489600 [5,3,2,2,1,1] => 4406400 [5,3,2,1,1,1,1] => 41860800 [5,3,1,1,1,1,1,1] => 418608000 [5,2,2,2,2,1] => 5875200 [5,2,2,2,1,1,1] => 55814400 [5,2,2,1,1,1,1,1] => 558144000 [4,4,4,2] => 30720 [4,4,4,1,1] => 261120 [4,4,3,3] => 34560 [4,4,3,2,1] => 391680 [4,4,3,1,1,1] => 3525120 [4,4,2,2,2] => 522240 [4,4,2,2,1,1] => 4700160 [4,4,2,1,1,1,1] => 44651520 [4,4,1,1,1,1,1,1] => 446515200 [4,3,3,3,1] => 440640 [4,3,3,2,2] => 587520 [4,3,3,2,1,1] => 5287680 [4,3,3,1,1,1,1] => 50232960 [4,3,2,2,2,1] => 7050240 [4,3,2,2,1,1,1] => 66977280 [4,3,2,1,1,1,1,1] => 669772800 [4,2,2,2,2,2] => 9400320 [4,2,2,2,2,1,1] => 89303040 [4,2,2,2,1,1,1,1] => 893030400 [3,3,3,3,2] => 660960 [3,3,3,3,1,1] => 5948640 [3,3,3,2,2,1] => 7931520 [3,3,3,2,1,1,1] => 75349440 [3,3,3,1,1,1,1,1] => 753494400 [3,3,2,2,2,2] => 10575360 [3,3,2,2,2,1,1] => 100465920 [3,3,2,2,1,1,1,1] => 1004659200 [3,2,2,2,2,2,1] => 133954560 [3,2,2,2,2,1,1,1] => 1339545600 [2,2,2,2,2,2,2] => 178606080 [2,2,2,2,2,2,1,1] => 1786060800 [15] => 1 [14,1] => 14 [13,2] => 26 [13,1,1] => 208 [12,3] => 36 [12,2,1] => 384 [12,1,1,1] => 3264 [11,4] => 44 [11,3,1] => 528 [11,2,2] => 704 [11,2,1,1] => 5984 [11,1,1,1,1] => 53856 [10,5] => 50 [10,4,1] => 640 [10,3,2] => 960 [10,3,1,1] => 8160 [10,2,2,1] => 10880 [10,2,1,1,1] => 97920 [10,1,1,1,1,1] => 930240 [9,6] => 54 [9,5,1] => 720 [9,4,2] => 1152 [9,4,1,1] => 9792 [9,3,3] => 1296 [9,3,2,1] => 14688 [9,3,1,1,1] => 132192 [9,2,2,2] => 19584 [9,2,2,1,1] => 176256 [9,2,1,1,1,1] => 1674432 [9,1,1,1,1,1,1] => 16744320 [8,7] => 56 [8,6,1] => 768 [8,5,2] => 1280 [8,5,1,1] => 10880 [8,4,3] => 1536 [8,4,2,1] => 17408 [8,4,1,1,1] => 156672 [8,3,3,1] => 19584 [8,3,2,2] => 26112 [8,3,2,1,1] => 235008 [8,3,1,1,1,1] => 2232576 [8,2,2,2,1] => 313344 [8,2,2,1,1,1] => 2976768 [8,2,1,1,1,1,1] => 29767680 [8,1,1,1,1,1,1,1] => 312560640 [7,7,1] => 784 [7,6,2] => 1344 [7,6,1,1] => 11424 [7,5,3] => 1680 [7,5,2,1] => 19040 [7,5,1,1,1] => 171360 [7,4,4] => 1792 [7,4,3,1] => 22848 [7,4,2,2] => 30464 [7,4,2,1,1] => 274176 [7,4,1,1,1,1] => 2604672 [7,3,3,2] => 34272 [7,3,3,1,1] => 308448 [7,3,2,2,1] => 411264 [7,3,2,1,1,1] => 3907008 [7,3,1,1,1,1,1] => 39070080 [7,2,2,2,2] => 548352 [7,2,2,2,1,1] => 5209344 [7,2,2,1,1,1,1] => 52093440 [7,2,1,1,1,1,1,1] => 546981120 [6,6,3] => 1728 [6,6,2,1] => 19584 [6,6,1,1,1] => 176256 [6,5,4] => 1920 [6,5,3,1] => 24480 [6,5,2,2] => 32640 [6,5,2,1,1] => 293760 [6,5,1,1,1,1] => 2790720 [6,4,4,1] => 26112 [6,4,3,2] => 39168 [6,4,3,1,1] => 352512 [6,4,2,2,1] => 470016 [6,4,2,1,1,1] => 4465152 [6,4,1,1,1,1,1] => 44651520 [6,3,3,3] => 44064 [6,3,3,2,1] => 528768 [6,3,3,1,1,1] => 5023296 [6,3,2,2,2] => 705024 [6,3,2,2,1,1] => 6697728 [6,3,2,1,1,1,1] => 66977280 [6,3,1,1,1,1,1,1] => 703261440 [6,2,2,2,2,1] => 8930304 [6,2,2,2,1,1,1] => 89303040 [6,2,2,1,1,1,1,1] => 937681920 [5,5,5] => 2000 [5,5,4,1] => 27200 [5,5,3,2] => 40800 [5,5,3,1,1] => 367200 [5,5,2,2,1] => 489600 [5,5,2,1,1,1] => 4651200 [5,5,1,1,1,1,1] => 46512000 [5,4,4,2] => 43520 [5,4,4,1,1] => 391680 [5,4,3,3] => 48960 [5,4,3,2,1] => 587520 [5,4,3,1,1,1] => 5581440 [5,4,2,2,2] => 783360 [5,4,2,2,1,1] => 7441920 [5,4,2,1,1,1,1] => 74419200 [5,4,1,1,1,1,1,1] => 781401600 [5,3,3,3,1] => 660960 [5,3,3,2,2] => 881280 [5,3,3,2,1,1] => 8372160 [5,3,3,1,1,1,1] => 83721600 [5,3,2,2,2,1] => 11162880 [5,3,2,2,1,1,1] => 111628800 [5,3,2,1,1,1,1,1] => 1172102400 [5,2,2,2,2,2] => 14883840 [5,2,2,2,2,1,1] => 148838400 [5,2,2,2,1,1,1,1] => 1562803200 [4,4,4,3] => 52224 [4,4,4,2,1] => 626688 [4,4,4,1,1,1] => 5953536 [4,4,3,3,1] => 705024 [4,4,3,2,2] => 940032 [4,4,3,2,1,1] => 8930304 [4,4,3,1,1,1,1] => 89303040 [4,4,2,2,2,1] => 11907072 [4,4,2,2,1,1,1] => 119070720 [4,4,2,1,1,1,1,1] => 1250242560 [4,3,3,3,2] => 1057536 [4,3,3,3,1,1] => 10046592 [4,3,3,2,2,1] => 13395456 [4,3,3,2,1,1,1] => 133954560 [4,3,3,1,1,1,1,1] => 1406522880 [4,3,2,2,2,2] => 17860608 [4,3,2,2,2,1,1] => 178606080 [4,3,2,2,1,1,1,1] => 1875363840 [4,2,2,2,2,2,1] => 238141440 [3,3,3,3,3] => 1189728 [3,3,3,3,2,1] => 15069888 [3,3,3,3,1,1,1] => 150698880 [3,3,3,2,2,2] => 20093184 [3,3,3,2,2,1,1] => 200931840 [3,3,3,2,1,1,1,1] => 2109784320 [3,3,2,2,2,2,1] => 267909120 [3,2,2,2,2,2,2] => 357212160 [16] => 1 [15,1] => 15 [14,2] => 28 [14,1,1] => 238 [13,3] => 39 [13,2,1] => 442 [13,1,1,1] => 3978 [12,4] => 48 [12,3,1] => 612 [12,2,2] => 816 [12,2,1,1] => 7344 [12,1,1,1,1] => 69768 [11,5] => 55 [11,4,1] => 748 [11,3,2] => 1122 [11,3,1,1] => 10098 [11,2,2,1] => 13464 [11,2,1,1,1] => 127908 [11,1,1,1,1,1] => 1279080 [10,6] => 60 [10,5,1] => 850 [10,4,2] => 1360 [10,4,1,1] => 12240 [10,3,3] => 1530 [10,3,2,1] => 18360 [10,3,1,1,1] => 174420 [10,2,2,2] => 24480 [10,2,2,1,1] => 232560 [10,2,1,1,1,1] => 2325600 [10,1,1,1,1,1,1] => 24418800 [9,7] => 63 [9,6,1] => 918 [9,5,2] => 1530 [9,5,1,1] => 13770 [9,4,3] => 1836 [9,4,2,1] => 22032 [9,4,1,1,1] => 209304 [9,3,3,1] => 24786 [9,3,2,2] => 33048 [9,3,2,1,1] => 313956 [9,3,1,1,1,1] => 3139560 [9,2,2,2,1] => 418608 [9,2,2,1,1,1] => 4186080 [9,2,1,1,1,1,1] => 43953840 [9,1,1,1,1,1,1,1] => 483492240 [8,8] => 64 [8,7,1] => 952 [8,6,2] => 1632 [8,6,1,1] => 14688 [8,5,3] => 2040 [8,5,2,1] => 24480 [8,5,1,1,1] => 232560 [8,4,4] => 2176 [8,4,3,1] => 29376 [8,4,2,2] => 39168 [8,4,2,1,1] => 372096 [8,4,1,1,1,1] => 3720960 [8,3,3,2] => 44064 [8,3,3,1,1] => 418608 [8,3,2,2,1] => 558144 [8,3,2,1,1,1] => 5581440 [8,3,1,1,1,1,1] => 58605120 [8,2,2,2,2] => 744192 [8,2,2,2,1,1] => 7441920 [8,2,2,1,1,1,1] => 78140160 [8,2,1,1,1,1,1,1] => 859541760 [7,7,2] => 1666 [7,7,1,1] => 14994 [7,6,3] => 2142 [7,6,2,1] => 25704 [7,6,1,1,1] => 244188 [7,5,4] => 2380 [7,5,3,1] => 32130 [7,5,2,2] => 42840 [7,5,2,1,1] => 406980 [7,5,1,1,1,1] => 4069800 [7,4,4,1] => 34272 [7,4,3,2] => 51408 [7,4,3,1,1] => 488376 [7,4,2,2,1] => 651168 [7,4,2,1,1,1] => 6511680 [7,4,1,1,1,1,1] => 68372640 [7,3,3,3] => 57834 [7,3,3,2,1] => 732564 [7,3,3,1,1,1] => 7325640 [7,3,2,2,2] => 976752 [7,3,2,2,1,1] => 9767520 [7,3,2,1,1,1,1] => 102558960 [7,3,1,1,1,1,1,1] => 1128148560 [7,2,2,2,2,1] => 13023360 [7,2,2,2,1,1,1] => 136745280 [7,2,2,1,1,1,1,1] => 1504198080 [6,6,4] => 2448 [6,6,3,1] => 33048 [6,6,2,2] => 44064 [6,6,2,1,1] => 418608 [6,6,1,1,1,1] => 4186080 [6,5,5] => 2550 [6,5,4,1] => 36720 [6,5,3,2] => 55080 [6,5,3,1,1] => 523260 [6,5,2,2,1] => 697680 [6,5,2,1,1,1] => 6976800 [6,5,1,1,1,1,1] => 73256400 [6,4,4,2] => 58752 [6,4,4,1,1] => 558144 [6,4,3,3] => 66096 [6,4,3,2,1] => 837216 [6,4,3,1,1,1] => 8372160 [6,4,2,2,2] => 1116288 [6,4,2,2,1,1] => 11162880 [6,4,2,1,1,1,1] => 117210240 [6,4,1,1,1,1,1,1] => 1289312640 [6,3,3,3,1] => 941868 [6,3,3,2,2] => 1255824 [6,3,3,2,1,1] => 12558240 [6,3,3,1,1,1,1] => 131861520 [6,3,2,2,2,1] => 16744320 [6,3,2,2,1,1,1] => 175815360 [6,3,2,1,1,1,1,1] => 1933968960 [6,2,2,2,2,2] => 22325760 [6,2,2,2,2,1,1] => 234420480 [5,5,5,1] => 38250 [5,5,4,2] => 61200 [5,5,4,1,1] => 581400 [5,5,3,3] => 68850 [5,5,3,2,1] => 872100 [5,5,3,1,1,1] => 8721000 [5,5,2,2,2] => 1162800 [5,5,2,2,1,1] => 11628000 [5,5,2,1,1,1,1] => 122094000 [5,5,1,1,1,1,1,1] => 1343034000 [5,4,4,3] => 73440 [5,4,4,2,1] => 930240 [5,4,4,1,1,1] => 9302400 [5,4,3,3,1] => 1046520 [5,4,3,2,2] => 1395360 [5,4,3,2,1,1] => 13953600 [5,4,3,1,1,1,1] => 146512800 [5,4,2,2,2,1] => 18604800 [5,4,2,2,1,1,1] => 195350400 [5,3,3,3,2] => 1569780 [5,3,3,3,1,1] => 15697800 [5,3,3,2,2,1] => 20930400 [5,3,3,2,1,1,1] => 219769200 [5,3,2,2,2,2] => 27907200 [5,3,2,2,2,1,1] => 293025600 [5,2,2,2,2,2,1] => 390700800 [4,4,4,4] => 78336 [4,4,4,3,1] => 1116288 [4,4,4,2,2] => 1488384 [4,4,4,2,1,1] => 14883840 [4,4,4,1,1,1,1] => 156280320 [4,4,3,3,2] => 1674432 [4,4,3,3,1,1] => 16744320 [4,4,3,2,2,1] => 22325760 [4,4,3,2,1,1,1] => 234420480 [4,4,2,2,2,2] => 29767680 [4,4,2,2,2,1,1] => 312560640 [4,3,3,3,3] => 1883736 [4,3,3,3,2,1] => 25116480 [4,3,3,3,1,1,1] => 263723040 [4,3,3,2,2,2] => 33488640 [4,3,3,2,2,1,1] => 351630720 [4,3,2,2,2,2,1] => 468840960 [4,2,2,2,2,2,2] => 625121280 [3,3,3,3,3,1] => 28256040 [3,3,3,3,2,2] => 37674720 [3,3,3,3,2,1,1] => 395584560 [3,3,3,2,2,2,1] => 527446080 [3,3,2,2,2,2,2] => 703261440 [17] => 1 [16,1] => 16 [15,2] => 30 [15,1,1] => 270 [14,3] => 42 [14,2,1] => 504 [14,1,1,1] => 4788 [13,4] => 52 [13,3,1] => 702 [13,2,2] => 936 [13,2,1,1] => 8892 [13,1,1,1,1] => 88920 [12,5] => 60 [12,4,1] => 864 [12,3,2] => 1296 [12,3,1,1] => 12312 [12,2,2,1] => 16416 [12,2,1,1,1] => 164160 [12,1,1,1,1,1] => 1723680 [11,6] => 66 [11,5,1] => 990 [11,4,2] => 1584 [11,4,1,1] => 15048 [11,3,3] => 1782 [11,3,2,1] => 22572 [11,3,1,1,1] => 225720 [11,2,2,2] => 30096 [11,2,2,1,1] => 300960 [11,2,1,1,1,1] => 3160080 [11,1,1,1,1,1,1] => 34760880 [10,7] => 70 [10,6,1] => 1080 [10,5,2] => 1800 [10,5,1,1] => 17100 [10,4,3] => 2160 [10,4,2,1] => 27360 [10,4,1,1,1] => 273600 [10,3,3,1] => 30780 [10,3,2,2] => 41040 [10,3,2,1,1] => 410400 [10,3,1,1,1,1] => 4309200 [10,2,2,2,1] => 547200 [10,2,2,1,1,1] => 5745600 [10,2,1,1,1,1,1] => 63201600 [10,1,1,1,1,1,1,1] => 726818400 [9,8] => 72 [9,7,1] => 1134 [9,6,2] => 1944 [9,6,1,1] => 18468 [9,5,3] => 2430 [9,5,2,1] => 30780 [9,5,1,1,1] => 307800 [9,4,4] => 2592 [9,4,3,1] => 36936 [9,4,2,2] => 49248 [9,4,2,1,1] => 492480 [9,4,1,1,1,1] => 5171040 [9,3,3,2] => 55404 [9,3,3,1,1] => 554040 [9,3,2,2,1] => 738720 [9,3,2,1,1,1] => 7756560 [9,3,1,1,1,1,1] => 85322160 [9,2,2,2,2] => 984960 [9,2,2,2,1,1] => 10342080 [9,2,2,1,1,1,1] => 113762880 [9,2,1,1,1,1,1,1] => 1308273120 [8,8,1] => 1152 [8,7,2] => 2016 [8,7,1,1] => 19152 [8,6,3] => 2592 [8,6,2,1] => 32832 [8,6,1,1,1] => 328320 [8,5,4] => 2880 [8,5,3,1] => 41040 [8,5,2,2] => 54720 [8,5,2,1,1] => 547200 [8,5,1,1,1,1] => 5745600 [8,4,4,1] => 43776 [8,4,3,2] => 65664 [8,4,3,1,1] => 656640 [8,4,2,2,1] => 875520 [8,4,2,1,1,1] => 9192960 [8,4,1,1,1,1,1] => 101122560 [8,3,3,3] => 73872 [8,3,3,2,1] => 984960 [8,3,3,1,1,1] => 10342080 [8,3,2,2,2] => 1313280 [8,3,2,2,1,1] => 13789440 [8,3,2,1,1,1,1] => 151683840 [8,3,1,1,1,1,1,1] => 1744364160 [8,2,2,2,2,1] => 18385920 [8,2,2,2,1,1,1] => 202245120 [7,7,3] => 2646 [7,7,2,1] => 33516 [7,7,1,1,1] => 335160 [7,6,4] => 3024 [7,6,3,1] => 43092 [7,6,2,2] => 57456 [7,6,2,1,1] => 574560 [7,6,1,1,1,1] => 6032880 [7,5,5] => 3150 [7,5,4,1] => 47880 [7,5,3,2] => 71820 [7,5,3,1,1] => 718200 [7,5,2,2,1] => 957600 [7,5,2,1,1,1] => 10054800 [7,5,1,1,1,1,1] => 110602800 [7,4,4,2] => 76608 [7,4,4,1,1] => 766080 [7,4,3,3] => 86184 [7,4,3,2,1] => 1149120 [7,4,3,1,1,1] => 12065760 [7,4,2,2,2] => 1532160 [7,4,2,2,1,1] => 16087680 [7,4,2,1,1,1,1] => 176964480 [7,4,1,1,1,1,1,1] => 2035091520 [7,3,3,3,1] => 1292760 [7,3,3,2,2] => 1723680 [7,3,3,2,1,1] => 18098640 [7,3,3,1,1,1,1] => 199085040 [7,3,2,2,2,1] => 24131520 [7,3,2,2,1,1,1] => 265446720 [7,2,2,2,2,2] => 32175360 [7,2,2,2,2,1,1] => 353928960 [6,6,5] => 3240 [6,6,4,1] => 49248 [6,6,3,2] => 73872 [6,6,3,1,1] => 738720 [6,6,2,2,1] => 984960 [6,6,2,1,1,1] => 10342080 [6,6,1,1,1,1,1] => 113762880 [6,5,5,1] => 51300 [6,5,4,2] => 82080 [6,5,4,1,1] => 820800 [6,5,3,3] => 92340 [6,5,3,2,1] => 1231200 [6,5,3,1,1,1] => 12927600 [6,5,2,2,2] => 1641600 [6,5,2,2,1,1] => 17236800 [6,5,2,1,1,1,1] => 189604800 [6,4,4,3] => 98496 [6,4,4,2,1] => 1313280 [6,4,4,1,1,1] => 13789440 [6,4,3,3,1] => 1477440 [6,4,3,2,2] => 1969920 [6,4,3,2,1,1] => 20684160 [6,4,3,1,1,1,1] => 227525760 [6,4,2,2,2,1] => 27578880 [6,4,2,2,1,1,1] => 303367680 [6,3,3,3,2] => 2216160 [6,3,3,3,1,1] => 23269680 [6,3,3,2,2,1] => 31026240 [6,3,3,2,1,1,1] => 341288640 [6,3,2,2,2,2] => 41368320 [6,3,2,2,2,1,1] => 455051520 [6,2,2,2,2,2,1] => 606735360 [5,5,5,2] => 85500 [5,5,5,1,1] => 855000 [5,5,4,3] => 102600 [5,5,4,2,1] => 1368000 [5,5,4,1,1,1] => 14364000 [5,5,3,3,1] => 1539000 [5,5,3,2,2] => 2052000 [5,5,3,2,1,1] => 21546000 [5,5,3,1,1,1,1] => 237006000 [5,5,2,2,2,1] => 28728000 [5,5,2,2,1,1,1] => 316008000 [5,4,4,4] => 109440 [5,4,4,3,1] => 1641600 [5,4,4,2,2] => 2188800 [5,4,4,2,1,1] => 22982400 [5,4,4,1,1,1,1] => 252806400 [5,4,3,3,2] => 2462400 [5,4,3,3,1,1] => 25855200 [5,4,3,2,2,1] => 34473600 [5,4,3,2,1,1,1] => 379209600 [5,4,2,2,2,2] => 45964800 [5,4,2,2,2,1,1] => 505612800 [5,3,3,3,3] => 2770200 [5,3,3,3,2,1] => 38782800 [5,3,3,3,1,1,1] => 426610800 [5,3,3,2,2,2] => 51710400 [5,3,3,2,2,1,1] => 568814400 [5,3,2,2,2,2,1] => 758419200 [5,2,2,2,2,2,2] => 1011225600 [4,4,4,4,1] => 1751040 [4,4,4,3,2] => 2626560 [4,4,4,3,1,1] => 27578880 [4,4,4,2,2,1] => 36771840 [4,4,4,2,1,1,1] => 404490240 [4,4,3,3,3] => 2954880 [4,4,3,3,2,1] => 41368320 [4,4,3,3,1,1,1] => 455051520 [4,4,3,2,2,2] => 55157760 [4,4,3,2,2,1,1] => 606735360 [4,4,2,2,2,2,1] => 808980480 [4,3,3,3,3,1] => 46539360 [4,3,3,3,2,2] => 62052480 [4,3,3,3,2,1,1] => 682577280 [4,3,3,2,2,2,1] => 910103040 [4,3,2,2,2,2,2] => 1213470720 [3,3,3,3,3,2] => 69809040 [3,3,3,3,3,1,1] => 767899440 [3,3,3,3,2,2,1] => 1023865920 [3,3,3,2,2,2,2] => 1365154560 ----------------------------------------------------------------------------- Created: Dec 29, 2023 at 19:14 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Aug 05, 2024 at 22:55 by Martin Rubey