***************************************************************************** * 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: St001605 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of colourings of a cycle such that the multiplicities of colours are given by a partition. Two colourings are considered equal, if they are obtained by an action of the cyclic group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(mu): # h is the basis dual to m h = SymmetricFunctions(QQ).h() return CyclicPermutationGroup(mu.size()).cycle_index().scalar(h(mu)) ----------------------------------------------------------------------------- Statistic values: [3] => 1 [2,1] => 1 [1,1,1] => 2 [4] => 1 [3,1] => 1 [2,2] => 2 [2,1,1] => 3 [1,1,1,1] => 6 [5] => 1 [4,1] => 1 [3,2] => 2 [3,1,1] => 4 [2,2,1] => 6 [2,1,1,1] => 12 [1,1,1,1,1] => 24 [6] => 1 [5,1] => 1 [4,2] => 3 [4,1,1] => 5 [3,3] => 4 [3,2,1] => 10 [3,1,1,1] => 20 [2,2,2] => 16 [2,2,1,1] => 30 [2,1,1,1,1] => 60 [1,1,1,1,1,1] => 120 [7] => 1 [6,1] => 1 [5,2] => 3 [5,1,1] => 6 [4,3] => 5 [4,2,1] => 15 [4,1,1,1] => 30 [3,3,1] => 20 [3,2,2] => 30 [3,2,1,1] => 60 [3,1,1,1,1] => 120 [2,2,2,1] => 90 [2,2,1,1,1] => 180 [2,1,1,1,1,1] => 360 [1,1,1,1,1,1,1] => 720 [8] => 1 [7,1] => 1 [6,2] => 4 [6,1,1] => 7 [5,3] => 7 [5,2,1] => 21 [5,1,1,1] => 42 [4,4] => 10 [4,3,1] => 35 [4,2,2] => 54 [4,2,1,1] => 105 [4,1,1,1,1] => 210 [3,3,2] => 70 [3,3,1,1] => 140 [3,2,2,1] => 210 [3,2,1,1,1] => 420 [3,1,1,1,1,1] => 840 [2,2,2,2] => 318 [2,2,2,1,1] => 630 [2,2,1,1,1,1] => 1260 [2,1,1,1,1,1,1] => 2520 [1,1,1,1,1,1,1,1] => 5040 [9] => 1 [8,1] => 1 [7,2] => 4 [7,1,1] => 8 [6,3] => 10 [6,2,1] => 28 [6,1,1,1] => 56 [5,4] => 14 [5,3,1] => 56 [5,2,2] => 84 [5,2,1,1] => 168 [5,1,1,1,1] => 336 [4,4,1] => 70 [4,3,2] => 140 [4,3,1,1] => 280 [4,2,2,1] => 420 [4,2,1,1,1] => 840 [4,1,1,1,1,1] => 1680 [3,3,3] => 188 [3,3,2,1] => 560 [3,3,1,1,1] => 1120 [3,2,2,2] => 840 [3,2,2,1,1] => 1680 [3,2,1,1,1,1] => 3360 [3,1,1,1,1,1,1] => 6720 [2,2,2,2,1] => 2520 [2,2,2,1,1,1] => 5040 [2,2,1,1,1,1,1] => 10080 [2,1,1,1,1,1,1,1] => 20160 [1,1,1,1,1,1,1,1,1] => 40320 [10] => 1 [9,1] => 1 [8,2] => 5 [8,1,1] => 9 [7,3] => 12 [7,2,1] => 36 [7,1,1,1] => 72 [6,4] => 22 [6,3,1] => 84 [6,2,2] => 128 [6,2,1,1] => 252 [6,1,1,1,1] => 504 [5,5] => 26 [5,4,1] => 126 [5,3,2] => 252 [5,3,1,1] => 504 [5,2,2,1] => 756 [5,2,1,1,1] => 1512 [5,1,1,1,1,1] => 3024 [4,4,2] => 318 [4,4,1,1] => 630 [4,3,3] => 420 [4,3,2,1] => 1260 [4,3,1,1,1] => 2520 [4,2,2,2] => 1896 [4,2,2,1,1] => 3780 [4,2,1,1,1,1] => 7560 [4,1,1,1,1,1,1] => 15120 [3,3,3,1] => 1680 [3,3,2,2] => 2520 [3,3,2,1,1] => 5040 [3,3,1,1,1,1] => 10080 [3,2,2,2,1] => 7560 [3,2,2,1,1,1] => 15120 [3,2,1,1,1,1,1] => 30240 [3,1,1,1,1,1,1,1] => 60480 [2,2,2,2,2] => 11352 [2,2,2,2,1,1] => 22680 [2,2,2,1,1,1,1] => 45360 [2,2,1,1,1,1,1,1] => 90720 [2,1,1,1,1,1,1,1,1] => 181440 [1,1,1,1,1,1,1,1,1,1] => 362880 [11] => 1 [10,1] => 1 [9,2] => 5 [9,1,1] => 10 [8,3] => 15 [8,2,1] => 45 [8,1,1,1] => 90 [7,4] => 30 [7,3,1] => 120 [7,2,2] => 180 [7,2,1,1] => 360 [7,1,1,1,1] => 720 [6,5] => 42 [6,4,1] => 210 [6,3,2] => 420 [6,3,1,1] => 840 [6,2,2,1] => 1260 [6,2,1,1,1] => 2520 [6,1,1,1,1,1] => 5040 [5,5,1] => 252 [5,4,2] => 630 [5,4,1,1] => 1260 [5,3,3] => 840 [5,3,2,1] => 2520 [5,3,1,1,1] => 5040 [5,2,2,2] => 3780 [5,2,2,1,1] => 7560 [5,2,1,1,1,1] => 15120 [5,1,1,1,1,1,1] => 30240 [4,4,3] => 1050 [4,4,2,1] => 3150 [4,4,1,1,1] => 6300 [4,3,3,1] => 4200 [4,3,2,2] => 6300 [4,3,2,1,1] => 12600 [4,3,1,1,1,1] => 25200 [4,2,2,2,1] => 18900 [4,2,2,1,1,1] => 37800 [4,2,1,1,1,1,1] => 75600 [4,1,1,1,1,1,1,1] => 151200 [3,3,3,2] => 8400 [3,3,3,1,1] => 16800 [3,3,2,2,1] => 25200 [3,3,2,1,1,1] => 50400 [3,3,1,1,1,1,1] => 100800 [3,2,2,2,2] => 37800 [3,2,2,2,1,1] => 75600 [3,2,2,1,1,1,1] => 151200 [3,2,1,1,1,1,1,1] => 302400 [3,1,1,1,1,1,1,1,1] => 604800 [2,2,2,2,2,1] => 113400 [2,2,2,2,1,1,1] => 226800 [2,2,2,1,1,1,1,1] => 453600 [2,2,1,1,1,1,1,1,1] => 907200 [2,1,1,1,1,1,1,1,1,1] => 1814400 [1,1,1,1,1,1,1,1,1,1,1] => 3628800 [12] => 1 [11,1] => 1 [10,2] => 6 [10,1,1] => 11 [9,3] => 19 [9,2,1] => 55 [9,1,1,1] => 110 [8,4] => 43 [8,3,1] => 165 [8,2,2] => 250 [8,2,1,1] => 495 [8,1,1,1,1] => 990 [7,5] => 66 [7,4,1] => 330 [7,3,2] => 660 [7,3,1,1] => 1320 [7,2,2,1] => 1980 [7,2,1,1,1] => 3960 [7,1,1,1,1,1] => 7920 [6,6] => 80 [6,5,1] => 462 [6,4,2] => 1160 [6,4,1,1] => 2310 [6,3,3] => 1542 [6,3,2,1] => 4620 [6,3,1,1,1] => 9240 [6,2,2,2] => 6940 [6,2,2,1,1] => 13860 [6,2,1,1,1,1] => 27720 [6,1,1,1,1,1,1] => 55440 [5,5,2] => 1386 [5,5,1,1] => 2772 [5,4,3] => 2310 [5,4,2,1] => 6930 [5,4,1,1,1] => 13860 [5,3,3,1] => 9240 [5,3,2,2] => 13860 [5,3,2,1,1] => 27720 [5,3,1,1,1,1] => 55440 [5,2,2,2,1] => 41580 [5,2,2,1,1,1] => 83160 [5,2,1,1,1,1,1] => 166320 [5,1,1,1,1,1,1,1] => 332640 [4,4,4] => 2896 [4,4,3,1] => 11550 [4,4,2,2] => 17340 [4,4,2,1,1] => 34650 [4,4,1,1,1,1] => 69300 [4,3,3,2] => 23100 [4,3,3,1,1] => 46200 [4,3,2,2,1] => 69300 [4,3,2,1,1,1] => 138600 [4,3,1,1,1,1,1] => 277200 [4,2,2,2,2] => 103980 [4,2,2,2,1,1] => 207900 [4,2,2,1,1,1,1] => 415800 [4,2,1,1,1,1,1,1] => 831600 [4,1,1,1,1,1,1,1,1] => 1663200 [3,3,3,3] => 30804 [3,3,3,2,1] => 92400 [3,3,3,1,1,1] => 184800 [3,3,2,2,2] => 138600 [3,3,2,2,1,1] => 277200 [3,3,2,1,1,1,1] => 554400 [3,3,1,1,1,1,1,1] => 1108800 [3,2,2,2,2,1] => 415800 [3,2,2,2,1,1,1] => 831600 [3,2,2,1,1,1,1,1] => 1663200 [3,2,1,1,1,1,1,1,1] => 3326400 [3,1,1,1,1,1,1,1,1,1] => 6652800 [2,2,2,2,2,2] => 623760 [2,2,2,2,2,1,1] => 1247400 [2,2,2,2,1,1,1,1] => 2494800 [2,2,2,1,1,1,1,1,1] => 4989600 [2,2,1,1,1,1,1,1,1,1] => 9979200 [2,1,1,1,1,1,1,1,1,1,1] => 19958400 [1,1,1,1,1,1,1,1,1,1,1,1] => 39916800 [13] => 1 [12,1] => 1 [11,2] => 6 [11,1,1] => 12 [10,3] => 22 [10,2,1] => 66 [10,1,1,1] => 132 [9,4] => 55 [9,3,1] => 220 [9,2,2] => 330 [9,2,1,1] => 660 [9,1,1,1,1] => 1320 [8,5] => 99 [8,4,1] => 495 [8,3,2] => 990 [8,3,1,1] => 1980 [8,2,2,1] => 2970 [8,2,1,1,1] => 5940 [8,1,1,1,1,1] => 11880 [7,6] => 132 [7,5,1] => 792 [7,4,2] => 1980 [7,4,1,1] => 3960 [7,3,3] => 2640 [7,3,2,1] => 7920 [7,3,1,1,1] => 15840 [7,2,2,2] => 11880 [7,2,2,1,1] => 23760 [7,2,1,1,1,1] => 47520 [7,1,1,1,1,1,1] => 95040 [6,6,1] => 924 [6,5,2] => 2772 [6,5,1,1] => 5544 [6,4,3] => 4620 [6,4,2,1] => 13860 [6,4,1,1,1] => 27720 [6,3,3,1] => 18480 [6,3,2,2] => 27720 [6,3,2,1,1] => 55440 [6,3,1,1,1,1] => 110880 [6,2,2,2,1] => 83160 [6,2,2,1,1,1] => 166320 [6,2,1,1,1,1,1] => 332640 [6,1,1,1,1,1,1,1] => 665280 [5,5,3] => 5544 [5,5,2,1] => 16632 [5,5,1,1,1] => 33264 [5,4,4] => 6930 [5,4,3,1] => 27720 [5,4,2,2] => 41580 [5,4,2,1,1] => 83160 [5,4,1,1,1,1] => 166320 [5,3,3,2] => 55440 [5,3,3,1,1] => 110880 [5,3,2,2,1] => 166320 [5,3,2,1,1,1] => 332640 [5,3,1,1,1,1,1] => 665280 [5,2,2,2,2] => 249480 [5,2,2,2,1,1] => 498960 [5,2,2,1,1,1,1] => 997920 [5,2,1,1,1,1,1,1] => 1995840 [5,1,1,1,1,1,1,1,1] => 3991680 [4,4,4,1] => 34650 [4,4,3,2] => 69300 [4,4,3,1,1] => 138600 [4,4,2,2,1] => 207900 [4,4,2,1,1,1] => 415800 [4,4,1,1,1,1,1] => 831600 [4,3,3,3] => 92400 [4,3,3,2,1] => 277200 [4,3,3,1,1,1] => 554400 [4,3,2,2,2] => 415800 [4,3,2,2,1,1] => 831600 [4,3,2,1,1,1,1] => 1663200 [4,3,1,1,1,1,1,1] => 3326400 [4,2,2,2,2,1] => 1247400 [4,2,2,2,1,1,1] => 2494800 [4,2,2,1,1,1,1,1] => 4989600 [4,2,1,1,1,1,1,1,1] => 9979200 [4,1,1,1,1,1,1,1,1,1] => 19958400 [3,3,3,3,1] => 369600 [3,3,3,2,2] => 554400 [3,3,3,2,1,1] => 1108800 [3,3,3,1,1,1,1] => 2217600 [3,3,2,2,2,1] => 1663200 [3,3,2,2,1,1,1] => 3326400 [3,3,2,1,1,1,1,1] => 6652800 [3,3,1,1,1,1,1,1,1] => 13305600 [3,2,2,2,2,2] => 2494800 [3,2,2,2,2,1,1] => 4989600 [3,2,2,2,1,1,1,1] => 9979200 [3,2,2,1,1,1,1,1,1] => 19958400 [3,2,1,1,1,1,1,1,1,1] => 39916800 [3,1,1,1,1,1,1,1,1,1,1] => 79833600 [2,2,2,2,2,2,1] => 7484400 [2,2,2,2,2,1,1,1] => 14968800 [2,2,2,2,1,1,1,1,1] => 29937600 [2,2,2,1,1,1,1,1,1,1] => 59875200 [2,2,1,1,1,1,1,1,1,1,1] => 119750400 [2,1,1,1,1,1,1,1,1,1,1,1] => 239500800 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 479001600 [14] => 1 [13,1] => 1 [12,2] => 7 [12,1,1] => 13 [11,3] => 26 [11,2,1] => 78 [11,1,1,1] => 156 [10,4] => 73 [10,3,1] => 286 [10,2,2] => 432 [10,2,1,1] => 858 [10,1,1,1,1] => 1716 [9,5] => 143 [9,4,1] => 715 [9,3,2] => 1430 [9,3,1,1] => 2860 [9,2,2,1] => 4290 [9,2,1,1,1] => 8580 [9,1,1,1,1,1] => 17160 [8,6] => 217 [8,5,1] => 1287 [8,4,2] => 3225 [8,4,1,1] => 6435 [8,3,3] => 4290 [8,3,2,1] => 12870 [8,3,1,1,1] => 25740 [8,2,2,2] => 19320 [8,2,2,1,1] => 38610 [8,2,1,1,1,1] => 77220 [8,1,1,1,1,1,1] => 154440 [7,7] => 246 [7,6,1] => 1716 [7,5,2] => 5148 [7,5,1,1] => 10296 [7,4,3] => 8580 [7,4,2,1] => 25740 [7,4,1,1,1] => 51480 [7,3,3,1] => 34320 [7,3,2,2] => 51480 [7,3,2,1,1] => 102960 [7,3,1,1,1,1] => 205920 [7,2,2,2,1] => 154440 [7,2,2,1,1,1] => 308880 [7,2,1,1,1,1,1] => 617760 [7,1,1,1,1,1,1,1] => 1235520 [6,6,2] => 6016 [6,6,1,1] => 12012 [6,5,3] => 12012 [6,5,2,1] => 36036 [6,5,1,1,1] => 72072 [6,4,4] => 15030 [6,4,3,1] => 60060 [6,4,2,2] => 90120 [6,4,2,1,1] => 180180 [6,4,1,1,1,1] => 360360 [6,3,3,2] => 120120 [6,3,3,1,1] => 240240 [6,3,2,2,1] => 360360 [6,3,2,1,1,1] => 720720 [6,3,1,1,1,1,1] => 1441440 [6,2,2,2,2] => 540600 [6,2,2,2,1,1] => 1081080 [6,2,2,1,1,1,1] => 2162160 [6,2,1,1,1,1,1,1] => 4324320 [6,1,1,1,1,1,1,1,1] => 8648640 [5,5,4] => 18018 [5,5,3,1] => 72072 [5,5,2,2] => 108108 [5,5,2,1,1] => 216216 [5,5,1,1,1,1] => 432432 [5,4,4,1] => 90090 [5,4,3,2] => 180180 [5,4,3,1,1] => 360360 [5,4,2,2,1] => 540540 [5,4,2,1,1,1] => 1081080 [5,4,1,1,1,1,1] => 2162160 [5,3,3,3] => 240240 [5,3,3,2,1] => 720720 [5,3,3,1,1,1] => 1441440 [5,3,2,2,2] => 1081080 [5,3,2,2,1,1] => 2162160 [5,3,2,1,1,1,1] => 4324320 [5,3,1,1,1,1,1,1] => 8648640 [5,2,2,2,2,1] => 3243240 [5,2,2,2,1,1,1] => 6486480 [5,2,2,1,1,1,1,1] => 12972960 [5,2,1,1,1,1,1,1,1] => 25945920 [5,1,1,1,1,1,1,1,1,1] => 51891840 [4,4,4,2] => 225270 [4,4,4,1,1] => 450450 [4,4,3,3] => 300300 [4,4,3,2,1] => 900900 [4,4,3,1,1,1] => 1801800 [4,4,2,2,2] => 1351440 [4,4,2,2,1,1] => 2702700 [4,4,2,1,1,1,1] => 5405400 [4,4,1,1,1,1,1,1] => 10810800 [4,3,3,3,1] => 1201200 [4,3,3,2,2] => 1801800 [4,3,3,2,1,1] => 3603600 [4,3,3,1,1,1,1] => 7207200 [4,3,2,2,2,1] => 5405400 [4,3,2,2,1,1,1] => 10810800 [4,3,2,1,1,1,1,1] => 21621600 [4,3,1,1,1,1,1,1,1] => 43243200 [4,2,2,2,2,2] => 8108280 [4,2,2,2,2,1,1] => 16216200 [4,2,2,2,1,1,1,1] => 32432400 [4,2,2,1,1,1,1,1,1] => 64864800 [4,2,1,1,1,1,1,1,1,1] => 129729600 [4,1,1,1,1,1,1,1,1,1,1] => 259459200 [3,3,3,3,2] => 2402400 [3,3,3,3,1,1] => 4804800 [3,3,3,2,2,1] => 7207200 [3,3,3,2,1,1,1] => 14414400 [3,3,3,1,1,1,1,1] => 28828800 [3,3,2,2,2,2] => 10810800 [3,3,2,2,2,1,1] => 21621600 [3,3,2,2,1,1,1,1] => 43243200 [3,3,2,1,1,1,1,1,1] => 86486400 [3,3,1,1,1,1,1,1,1,1] => 172972800 [3,2,2,2,2,2,1] => 32432400 [3,2,2,2,2,1,1,1] => 64864800 [3,2,2,2,1,1,1,1,1] => 129729600 [3,2,2,1,1,1,1,1,1,1] => 259459200 [3,2,1,1,1,1,1,1,1,1,1] => 518918400 [3,1,1,1,1,1,1,1,1,1,1,1] => 1037836800 [2,2,2,2,2,2,2] => 48648960 [2,2,2,2,2,2,1,1] => 97297200 [2,2,2,2,2,1,1,1,1] => 194594400 [2,2,2,2,1,1,1,1,1,1] => 389188800 [2,2,2,1,1,1,1,1,1,1,1] => 778377600 [2,2,1,1,1,1,1,1,1,1,1,1] => 1556755200 [15] => 1 [14,1] => 1 [13,2] => 7 [13,1,1] => 14 [12,3] => 31 [12,2,1] => 91 [12,1,1,1] => 182 [11,4] => 91 [11,3,1] => 364 [11,2,2] => 546 [11,2,1,1] => 1092 [11,1,1,1,1] => 2184 [10,5] => 201 [10,4,1] => 1001 [10,3,2] => 2002 [10,3,1,1] => 4004 [10,2,2,1] => 6006 [10,2,1,1,1] => 12012 [10,1,1,1,1,1] => 24024 [9,6] => 335 [9,5,1] => 2002 [9,4,2] => 5005 [9,4,1,1] => 10010 [9,3,3] => 6676 [9,3,2,1] => 20020 [9,3,1,1,1] => 40040 [9,2,2,2] => 30030 [9,2,2,1,1] => 60060 [9,2,1,1,1,1] => 120120 [9,1,1,1,1,1,1] => 240240 [8,7] => 429 [8,6,1] => 3003 [8,5,2] => 9009 [8,5,1,1] => 18018 [8,4,3] => 15015 [8,4,2,1] => 45045 [8,4,1,1,1] => 90090 [8,3,3,1] => 60060 [8,3,2,2] => 90090 [8,3,2,1,1] => 180180 [8,3,1,1,1,1] => 360360 [8,2,2,2,1] => 270270 [8,2,2,1,1,1] => 540540 [8,2,1,1,1,1,1] => 1081080 [8,1,1,1,1,1,1,1] => 2162160 [7,7,1] => 3432 [7,6,2] => 12012 [7,6,1,1] => 24024 [7,5,3] => 24024 [7,5,2,1] => 72072 [7,5,1,1,1] => 144144 [7,4,4] => 30030 [7,4,3,1] => 120120 [7,4,2,2] => 180180 [7,4,2,1,1] => 360360 [7,4,1,1,1,1] => 720720 [7,3,3,2] => 240240 [7,3,3,1,1] => 480480 [7,3,2,2,1] => 720720 [7,3,2,1,1,1] => 1441440 [7,3,1,1,1,1,1] => 2882880 [7,2,2,2,2] => 1081080 [7,2,2,2,1,1] => 2162160 [7,2,2,1,1,1,1] => 4324320 [7,2,1,1,1,1,1,1] => 8648640 [7,1,1,1,1,1,1,1,1] => 17297280 [6,6,3] => 28032 [6,6,2,1] => 84084 [6,6,1,1,1] => 168168 [6,5,4] => 42042 [6,5,3,1] => 168168 [6,5,2,2] => 252252 [6,5,2,1,1] => 504504 [6,5,1,1,1,1] => 1009008 [6,4,4,1] => 210210 [6,4,3,2] => 420420 [6,4,3,1,1] => 840840 [6,4,2,2,1] => 1261260 [6,4,2,1,1,1] => 2522520 [6,4,1,1,1,1,1] => 5045040 [6,3,3,3] => 560568 [6,3,3,2,1] => 1681680 [6,3,3,1,1,1] => 3363360 [6,3,2,2,2] => 2522520 [6,3,2,2,1,1] => 5045040 [6,3,2,1,1,1,1] => 10090080 [6,3,1,1,1,1,1,1] => 20180160 [6,2,2,2,2,1] => 7567560 [6,2,2,2,1,1,1] => 15135120 [6,2,2,1,1,1,1,1] => 30270240 [6,2,1,1,1,1,1,1,1] => 60540480 [6,1,1,1,1,1,1,1,1,1] => 121080960 [5,5,5] => 50452 [5,5,4,1] => 252252 [5,5,3,2] => 504504 [5,5,3,1,1] => 1009008 [5,5,2,2,1] => 1513512 [5,5,2,1,1,1] => 3027024 [5,5,1,1,1,1,1] => 6054048 [5,4,4,2] => 630630 [5,4,4,1,1] => 1261260 [5,4,3,3] => 840840 [5,4,3,2,1] => 2522520 [5,4,3,1,1,1] => 5045040 [5,4,2,2,2] => 3783780 [5,4,2,2,1,1] => 7567560 [5,4,2,1,1,1,1] => 15135120 [5,4,1,1,1,1,1,1] => 30270240 [5,3,3,3,1] => 3363360 [5,3,3,2,2] => 5045040 [5,3,3,2,1,1] => 10090080 [5,3,3,1,1,1,1] => 20180160 [5,3,2,2,2,1] => 15135120 [5,3,2,2,1,1,1] => 30270240 [5,3,2,1,1,1,1,1] => 60540480 [5,3,1,1,1,1,1,1,1] => 121080960 [5,2,2,2,2,2] => 22702680 [5,2,2,2,2,1,1] => 45405360 [5,2,2,2,1,1,1,1] => 90810720 [5,2,2,1,1,1,1,1,1] => 181621440 [5,2,1,1,1,1,1,1,1,1] => 363242880 [5,1,1,1,1,1,1,1,1,1,1] => 726485760 [4,4,4,3] => 1051050 [4,4,4,2,1] => 3153150 [4,4,4,1,1,1] => 6306300 [4,4,3,3,1] => 4204200 [4,4,3,2,2] => 6306300 [4,4,3,2,1,1] => 12612600 [4,4,3,1,1,1,1] => 25225200 [4,4,2,2,2,1] => 18918900 [4,4,2,2,1,1,1] => 37837800 [4,4,2,1,1,1,1,1] => 75675600 [4,4,1,1,1,1,1,1,1] => 151351200 [4,3,3,3,2] => 8408400 [4,3,3,3,1,1] => 16816800 [4,3,3,2,2,1] => 25225200 [4,3,3,2,1,1,1] => 50450400 [4,3,3,1,1,1,1,1] => 100900800 [4,3,2,2,2,2] => 37837800 [4,3,2,2,2,1,1] => 75675600 [4,3,2,2,1,1,1,1] => 151351200 [4,3,2,1,1,1,1,1,1] => 302702400 [4,3,1,1,1,1,1,1,1,1] => 605404800 [4,2,2,2,2,2,1] => 113513400 [4,2,2,2,2,1,1,1] => 227026800 [4,2,2,2,1,1,1,1,1] => 454053600 [4,2,2,1,1,1,1,1,1,1] => 908107200 [4,2,1,1,1,1,1,1,1,1,1] => 1816214400 [3,3,3,3,3] => 11211216 [3,3,3,3,2,1] => 33633600 [3,3,3,3,1,1,1] => 67267200 [3,3,3,2,2,2] => 50450400 [3,3,3,2,2,1,1] => 100900800 [3,3,3,2,1,1,1,1] => 201801600 [3,3,3,1,1,1,1,1,1] => 403603200 [3,3,2,2,2,2,1] => 151351200 [3,3,2,2,2,1,1,1] => 302702400 [3,3,2,2,1,1,1,1,1] => 605404800 [3,3,2,1,1,1,1,1,1,1] => 1210809600 [3,2,2,2,2,2,2] => 227026800 [3,2,2,2,2,2,1,1] => 454053600 [3,2,2,2,2,1,1,1,1] => 908107200 [3,2,2,2,1,1,1,1,1,1] => 1816214400 [2,2,2,2,2,2,2,1] => 681080400 [2,2,2,2,2,2,1,1,1] => 1362160800 [16] => 1 [15,1] => 1 [14,2] => 8 [14,1,1] => 15 [13,3] => 35 [13,2,1] => 105 [13,1,1,1] => 210 [12,4] => 116 [12,3,1] => 455 [12,2,2] => 686 [12,2,1,1] => 1365 [12,1,1,1,1] => 2730 [11,5] => 273 [11,4,1] => 1365 [11,3,2] => 2730 [11,3,1,1] => 5460 [11,2,2,1] => 8190 [11,2,1,1,1] => 16380 [11,1,1,1,1,1] => 32760 [10,6] => 504 [10,5,1] => 3003 [10,4,2] => 7518 [10,4,1,1] => 15015 [10,3,3] => 10010 [10,3,2,1] => 30030 [10,3,1,1,1] => 60060 [10,2,2,2] => 45066 [10,2,2,1,1] => 90090 [10,2,1,1,1,1] => 180180 [10,1,1,1,1,1,1] => 360360 [9,7] => 715 [9,6,1] => 5005 [9,5,2] => 15015 [9,5,1,1] => 30030 [9,4,3] => 25025 [9,4,2,1] => 75075 [9,4,1,1,1] => 150150 [9,3,3,1] => 100100 [9,3,2,2] => 150150 [9,3,2,1,1] => 300300 [9,3,1,1,1,1] => 600600 [9,2,2,2,1] => 450450 [9,2,2,1,1,1] => 900900 [9,2,1,1,1,1,1] => 1801800 [9,1,1,1,1,1,1,1] => 3603600 [8,8] => 810 [8,7,1] => 6435 [8,6,2] => 22540 [8,6,1,1] => 45045 [8,5,3] => 45045 [8,5,2,1] => 135135 [8,5,1,1,1] => 270270 [8,4,4] => 56334 [8,4,3,1] => 225225 [8,4,2,2] => 337890 [8,4,2,1,1] => 675675 [8,4,1,1,1,1] => 1351350 [8,3,3,2] => 450450 [8,3,3,1,1] => 900900 [8,3,2,2,1] => 1351350 [8,3,2,1,1,1] => 2702700 [8,3,1,1,1,1,1] => 5405400 [8,2,2,2,2] => 2027130 [8,2,2,2,1,1] => 4054050 [8,2,2,1,1,1,1] => 8108100 [8,2,1,1,1,1,1,1] => 16216200 [8,1,1,1,1,1,1,1,1] => 32432400 [7,7,2] => 25740 [7,7,1,1] => 51480 [7,6,3] => 60060 [7,6,2,1] => 180180 [7,6,1,1,1] => 360360 [7,5,4] => 90090 [7,5,3,1] => 360360 [7,5,2,2] => 540540 [7,5,2,1,1] => 1081080 [7,5,1,1,1,1] => 2162160 [7,4,4,1] => 450450 [7,4,3,2] => 900900 [7,4,3,1,1] => 1801800 [7,4,2,2,1] => 2702700 [7,4,2,1,1,1] => 5405400 [7,4,1,1,1,1,1] => 10810800 [7,3,3,3] => 1201200 [7,3,3,2,1] => 3603600 [7,3,3,1,1,1] => 7207200 [7,3,2,2,2] => 5405400 [7,3,2,2,1,1] => 10810800 [7,3,2,1,1,1,1] => 21621600 [7,3,1,1,1,1,1,1] => 43243200 [7,2,2,2,2,1] => 16216200 [7,2,2,2,1,1,1] => 32432400 [7,2,2,1,1,1,1,1] => 64864800 [7,2,1,1,1,1,1,1,1] => 129729600 [7,1,1,1,1,1,1,1,1,1] => 259459200 [6,6,4] => 105140 [6,6,3,1] => 420420 [6,6,2,2] => 630700 [6,6,2,1,1] => 1261260 [6,6,1,1,1,1] => 2522520 [6,5,5] => 126126 [6,5,4,1] => 630630 [6,5,3,2] => 1261260 [6,5,3,1,1] => 2522520 [6,5,2,2,1] => 3783780 [6,5,2,1,1,1] => 7567560 [6,5,1,1,1,1,1] => 15135120 [6,4,4,2] => 1576680 [6,4,4,1,1] => 3153150 [6,4,3,3] => 2102100 [6,4,3,2,1] => 6306300 [6,4,3,1,1,1] => 12612600 [6,4,2,2,2] => 9459660 [6,4,2,2,1,1] => 18918900 [6,4,2,1,1,1,1] => 37837800 [6,4,1,1,1,1,1,1] => 75675600 [6,3,3,3,1] => 8408400 [6,3,3,2,2] => 12612600 [6,3,3,2,1,1] => 25225200 [6,3,3,1,1,1,1] => 50450400 [6,3,2,2,2,1] => 37837800 [6,3,2,2,1,1,1] => 75675600 [6,3,2,1,1,1,1,1] => 151351200 [6,3,1,1,1,1,1,1,1] => 302702400 [6,2,2,2,2,2] => 56757120 [6,2,2,2,2,1,1] => 113513400 [6,2,2,2,1,1,1,1] => 227026800 [6,2,2,1,1,1,1,1,1] => 454053600 [6,2,1,1,1,1,1,1,1,1] => 908107200 [6,1,1,1,1,1,1,1,1,1,1] => 1816214400 [5,5,5,1] => 756756 [5,5,4,2] => 1891890 [5,5,4,1,1] => 3783780 [5,5,3,3] => 2522520 [5,5,3,2,1] => 7567560 [5,5,3,1,1,1] => 15135120 [5,5,2,2,2] => 11351340 [5,5,2,2,1,1] => 22702680 [5,5,2,1,1,1,1] => 45405360 [5,5,1,1,1,1,1,1] => 90810720 [5,4,4,3] => 3153150 [5,4,4,2,1] => 9459450 [5,4,4,1,1,1] => 18918900 [5,4,3,3,1] => 12612600 [5,4,3,2,2] => 18918900 [5,4,3,2,1,1] => 37837800 [5,4,3,1,1,1,1] => 75675600 [5,4,2,2,2,1] => 56756700 [5,4,2,2,1,1,1] => 113513400 [5,4,2,1,1,1,1,1] => 227026800 [5,4,1,1,1,1,1,1,1] => 454053600 [5,3,3,3,2] => 25225200 [5,3,3,3,1,1] => 50450400 [5,3,3,2,2,1] => 75675600 [5,3,3,2,1,1,1] => 151351200 [5,3,3,1,1,1,1,1] => 302702400 [5,3,2,2,2,2] => 113513400 [5,3,2,2,2,1,1] => 227026800 [5,3,2,2,1,1,1,1] => 454053600 [5,3,2,1,1,1,1,1,1] => 908107200 [5,3,1,1,1,1,1,1,1,1] => 1816214400 [5,2,2,2,2,2,1] => 340540200 [5,2,2,2,2,1,1,1] => 681080400 [5,2,2,2,1,1,1,1,1] => 1362160800 [4,4,4,4] => 3941598 [4,4,4,3,1] => 15765750 [4,4,4,2,2] => 23648940 [4,4,4,2,1,1] => 47297250 [4,4,4,1,1,1,1] => 94594500 [4,4,3,3,2] => 31531500 [4,4,3,3,1,1] => 63063000 [4,4,3,2,2,1] => 94594500 [4,4,3,2,1,1,1] => 189189000 [4,4,3,1,1,1,1,1] => 378378000 [4,4,2,2,2,2] => 141892380 [4,4,2,2,2,1,1] => 283783500 [4,4,2,2,1,1,1,1] => 567567000 [4,4,2,1,1,1,1,1,1] => 1135134000 [4,3,3,3,3] => 42042000 [4,3,3,3,2,1] => 126126000 [4,3,3,3,1,1,1] => 252252000 [4,3,3,2,2,2] => 189189000 [4,3,3,2,2,1,1] => 378378000 [4,3,3,2,1,1,1,1] => 756756000 [4,3,3,1,1,1,1,1,1] => 1513512000 [4,3,2,2,2,2,1] => 567567000 [4,3,2,2,2,1,1,1] => 1135134000 [4,2,2,2,2,2,2] => 851351760 [4,2,2,2,2,2,1,1] => 1702701000 [3,3,3,3,3,1] => 168168000 [3,3,3,3,2,2] => 252252000 [3,3,3,3,2,1,1] => 504504000 [3,3,3,3,1,1,1,1] => 1009008000 [3,3,3,2,2,2,1] => 756756000 [3,3,3,2,2,1,1,1] => 1513512000 [3,3,2,2,2,2,2] => 1135134000 [17] => 1 [16,1] => 1 [15,2] => 8 [15,1,1] => 16 [14,3] => 40 [14,2,1] => 120 [14,1,1,1] => 240 [13,4] => 140 [13,3,1] => 560 [13,2,2] => 840 [13,2,1,1] => 1680 [13,1,1,1,1] => 3360 [12,5] => 364 [12,4,1] => 1820 [12,3,2] => 3640 [12,3,1,1] => 7280 [12,2,2,1] => 10920 [12,2,1,1,1] => 21840 [12,1,1,1,1,1] => 43680 [11,6] => 728 [11,5,1] => 4368 [11,4,2] => 10920 [11,4,1,1] => 21840 [11,3,3] => 14560 [11,3,2,1] => 43680 [11,3,1,1,1] => 87360 [11,2,2,2] => 65520 [11,2,2,1,1] => 131040 [11,2,1,1,1,1] => 262080 [11,1,1,1,1,1,1] => 524160 [10,7] => 1144 [10,6,1] => 8008 [10,5,2] => 24024 [10,5,1,1] => 48048 [10,4,3] => 40040 [10,4,2,1] => 120120 [10,4,1,1,1] => 240240 [10,3,3,1] => 160160 [10,3,2,2] => 240240 [10,3,2,1,1] => 480480 [10,3,1,1,1,1] => 960960 [10,2,2,2,1] => 720720 [10,2,2,1,1,1] => 1441440 [10,2,1,1,1,1,1] => 2882880 [10,1,1,1,1,1,1,1] => 5765760 [9,8] => 1430 [9,7,1] => 11440 [9,6,2] => 40040 [9,6,1,1] => 80080 [9,5,3] => 80080 [9,5,2,1] => 240240 [9,5,1,1,1] => 480480 [9,4,4] => 100100 [9,4,3,1] => 400400 [9,4,2,2] => 600600 [9,4,2,1,1] => 1201200 [9,4,1,1,1,1] => 2402400 [9,3,3,2] => 800800 [9,3,3,1,1] => 1601600 [9,3,2,2,1] => 2402400 [9,3,2,1,1,1] => 4804800 [9,3,1,1,1,1,1] => 9609600 [9,2,2,2,2] => 3603600 [9,2,2,2,1,1] => 7207200 [9,2,2,1,1,1,1] => 14414400 [9,2,1,1,1,1,1,1] => 28828800 [9,1,1,1,1,1,1,1,1] => 57657600 [8,8,1] => 12870 [8,7,2] => 51480 [8,7,1,1] => 102960 [8,6,3] => 120120 [8,6,2,1] => 360360 [8,6,1,1,1] => 720720 [8,5,4] => 180180 [8,5,3,1] => 720720 [8,5,2,2] => 1081080 [8,5,2,1,1] => 2162160 [8,5,1,1,1,1] => 4324320 [8,4,4,1] => 900900 [8,4,3,2] => 1801800 [8,4,3,1,1] => 3603600 [8,4,2,2,1] => 5405400 [8,4,2,1,1,1] => 10810800 [8,4,1,1,1,1,1] => 21621600 [8,3,3,3] => 2402400 [8,3,3,2,1] => 7207200 [8,3,3,1,1,1] => 14414400 [8,3,2,2,2] => 10810800 [8,3,2,2,1,1] => 21621600 [8,3,2,1,1,1,1] => 43243200 [8,3,1,1,1,1,1,1] => 86486400 [8,2,2,2,2,1] => 32432400 [8,2,2,2,1,1,1] => 64864800 [8,2,2,1,1,1,1,1] => 129729600 [8,2,1,1,1,1,1,1,1] => 259459200 [8,1,1,1,1,1,1,1,1,1] => 518918400 [7,7,3] => 137280 [7,7,2,1] => 411840 [7,7,1,1,1] => 823680 [7,6,4] => 240240 [7,6,3,1] => 960960 [7,6,2,2] => 1441440 [7,6,2,1,1] => 2882880 [7,6,1,1,1,1] => 5765760 [7,5,5] => 288288 [7,5,4,1] => 1441440 [7,5,3,2] => 2882880 [7,5,3,1,1] => 5765760 [7,5,2,2,1] => 8648640 [7,5,2,1,1,1] => 17297280 [7,5,1,1,1,1,1] => 34594560 [7,4,4,2] => 3603600 [7,4,4,1,1] => 7207200 [7,4,3,3] => 4804800 [7,4,3,2,1] => 14414400 [7,4,3,1,1,1] => 28828800 [7,4,2,2,2] => 21621600 [7,4,2,2,1,1] => 43243200 [7,4,2,1,1,1,1] => 86486400 [7,4,1,1,1,1,1,1] => 172972800 [7,3,3,3,1] => 19219200 [7,3,3,2,2] => 28828800 [7,3,3,2,1,1] => 57657600 [7,3,3,1,1,1,1] => 115315200 [7,3,2,2,2,1] => 86486400 [7,3,2,2,1,1,1] => 172972800 [7,3,2,1,1,1,1,1] => 345945600 [7,3,1,1,1,1,1,1,1] => 691891200 [7,2,2,2,2,2] => 129729600 [7,2,2,2,2,1,1] => 259459200 [7,2,2,2,1,1,1,1] => 518918400 [7,2,2,1,1,1,1,1,1] => 1037836800 [7,2,1,1,1,1,1,1,1,1] => 2075673600 [6,6,5] => 336336 [6,6,4,1] => 1681680 [6,6,3,2] => 3363360 [6,6,3,1,1] => 6726720 [6,6,2,2,1] => 10090080 [6,6,2,1,1,1] => 20180160 [6,6,1,1,1,1,1] => 40360320 [6,5,5,1] => 2018016 [6,5,4,2] => 5045040 [6,5,4,1,1] => 10090080 [6,5,3,3] => 6726720 [6,5,3,2,1] => 20180160 [6,5,3,1,1,1] => 40360320 [6,5,2,2,2] => 30270240 [6,5,2,2,1,1] => 60540480 [6,5,2,1,1,1,1] => 121080960 [6,5,1,1,1,1,1,1] => 242161920 [6,4,4,3] => 8408400 [6,4,4,2,1] => 25225200 [6,4,4,1,1,1] => 50450400 [6,4,3,3,1] => 33633600 [6,4,3,2,2] => 50450400 [6,4,3,2,1,1] => 100900800 [6,4,3,1,1,1,1] => 201801600 [6,4,2,2,2,1] => 151351200 [6,4,2,2,1,1,1] => 302702400 [6,4,2,1,1,1,1,1] => 605404800 [6,4,1,1,1,1,1,1,1] => 1210809600 [6,3,3,3,2] => 67267200 [6,3,3,3,1,1] => 134534400 [6,3,3,2,2,1] => 201801600 [6,3,3,2,1,1,1] => 403603200 [6,3,3,1,1,1,1,1] => 807206400 [6,3,2,2,2,2] => 302702400 [6,3,2,2,2,1,1] => 605404800 [6,3,2,2,1,1,1,1] => 1210809600 [6,2,2,2,2,2,1] => 908107200 [6,2,2,2,2,1,1,1] => 1816214400 [5,5,5,2] => 6054048 [5,5,5,1,1] => 12108096 [5,5,4,3] => 10090080 [5,5,4,2,1] => 30270240 [5,5,4,1,1,1] => 60540480 [5,5,3,3,1] => 40360320 [5,5,3,2,2] => 60540480 [5,5,3,2,1,1] => 121080960 [5,5,3,1,1,1,1] => 242161920 [5,5,2,2,2,1] => 181621440 [5,5,2,2,1,1,1] => 363242880 [5,5,2,1,1,1,1,1] => 726485760 [5,5,1,1,1,1,1,1,1] => 1452971520 [5,4,4,4] => 12612600 [5,4,4,3,1] => 50450400 [5,4,4,2,2] => 75675600 [5,4,4,2,1,1] => 151351200 [5,4,4,1,1,1,1] => 302702400 [5,4,3,3,2] => 100900800 [5,4,3,3,1,1] => 201801600 [5,4,3,2,2,1] => 302702400 [5,4,3,2,1,1,1] => 605404800 [5,4,3,1,1,1,1,1] => 1210809600 [5,4,2,2,2,2] => 454053600 [5,4,2,2,2,1,1] => 908107200 [5,4,2,2,1,1,1,1] => 1816214400 [5,3,3,3,3] => 134534400 [5,3,3,3,2,1] => 403603200 [5,3,3,3,1,1,1] => 807206400 [5,3,3,2,2,2] => 605404800 [5,3,3,2,2,1,1] => 1210809600 [5,3,2,2,2,2,1] => 1816214400 [4,4,4,4,1] => 63063000 [4,4,4,3,2] => 126126000 [4,4,4,3,1,1] => 252252000 [4,4,4,2,2,1] => 378378000 [4,4,4,2,1,1,1] => 756756000 [4,4,4,1,1,1,1,1] => 1513512000 [4,4,3,3,3] => 168168000 [4,4,3,3,2,1] => 504504000 [4,4,3,3,1,1,1] => 1009008000 [4,4,3,2,2,2] => 756756000 [4,4,3,2,2,1,1] => 1513512000 [4,3,3,3,3,1] => 672672000 [4,3,3,3,2,2] => 1009008000 [4,3,3,3,2,1,1] => 2018016000 [3,3,3,3,3,2] => 1345344000 ----------------------------------------------------------------------------- Created: Sep 27, 2020 at 11:57 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 27, 2020 at 11:57 by Martin Rubey