***************************************************************************** * 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: St001603 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. Two colourings are considered equal, if they are obtained by an action of the dihedral 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 DihedralGroup(mu.size()).cycle_index().scalar(h(mu)) ----------------------------------------------------------------------------- Statistic values: [3] => 1 [2,1] => 1 [1,1,1] => 1 [4] => 1 [3,1] => 1 [2,2] => 2 [2,1,1] => 2 [1,1,1,1] => 3 [5] => 1 [4,1] => 1 [3,2] => 2 [3,1,1] => 2 [2,2,1] => 4 [2,1,1,1] => 6 [1,1,1,1,1] => 12 [6] => 1 [5,1] => 1 [4,2] => 3 [4,1,1] => 3 [3,3] => 3 [3,2,1] => 6 [3,1,1,1] => 10 [2,2,2] => 11 [2,2,1,1] => 16 [2,1,1,1,1] => 30 [1,1,1,1,1,1] => 60 [7] => 1 [6,1] => 1 [5,2] => 3 [5,1,1] => 3 [4,3] => 4 [4,2,1] => 9 [4,1,1,1] => 15 [3,3,1] => 10 [3,2,2] => 18 [3,2,1,1] => 30 [3,1,1,1,1] => 60 [2,2,2,1] => 48 [2,2,1,1,1] => 90 [2,1,1,1,1,1] => 180 [1,1,1,1,1,1,1] => 360 [8] => 1 [7,1] => 1 [6,2] => 4 [6,1,1] => 4 [5,3] => 5 [5,2,1] => 12 [5,1,1,1] => 21 [4,4] => 8 [4,3,1] => 19 [4,2,2] => 33 [4,2,1,1] => 54 [4,1,1,1,1] => 105 [3,3,2] => 38 [3,3,1,1] => 70 [3,2,2,1] => 108 [3,2,1,1,1] => 210 [3,1,1,1,1,1] => 420 [2,2,2,2] => 171 [2,2,2,1,1] => 318 [2,2,1,1,1,1] => 630 [2,1,1,1,1,1,1] => 1260 [1,1,1,1,1,1,1,1] => 2520 [9] => 1 [8,1] => 1 [7,2] => 4 [7,1,1] => 4 [6,3] => 7 [6,2,1] => 16 [6,1,1,1] => 28 [5,4] => 10 [5,3,1] => 28 [5,2,2] => 48 [5,2,1,1] => 84 [5,1,1,1,1] => 168 [4,4,1] => 38 [4,3,2] => 76 [4,3,1,1] => 140 [4,2,2,1] => 216 [4,2,1,1,1] => 420 [4,1,1,1,1,1] => 840 [3,3,3] => 94 [3,3,2,1] => 280 [3,3,1,1,1] => 560 [3,2,2,2] => 432 [3,2,2,1,1] => 840 [3,2,1,1,1,1] => 1680 [3,1,1,1,1,1,1] => 3360 [2,2,2,2,1] => 1272 [2,2,2,1,1,1] => 2520 [2,2,1,1,1,1,1] => 5040 [2,1,1,1,1,1,1,1] => 10080 [1,1,1,1,1,1,1,1,1] => 20160 [10] => 1 [9,1] => 1 [8,2] => 5 [8,1,1] => 5 [7,3] => 8 [7,2,1] => 20 [7,1,1,1] => 36 [6,4] => 16 [6,3,1] => 44 [6,2,2] => 74 [6,2,1,1] => 128 [6,1,1,1,1] => 252 [5,5] => 16 [5,4,1] => 66 [5,3,2] => 132 [5,3,1,1] => 252 [5,2,2,1] => 384 [5,2,1,1,1] => 756 [5,1,1,1,1,1] => 1512 [4,4,2] => 174 [4,4,1,1] => 318 [4,3,3] => 216 [4,3,2,1] => 636 [4,3,1,1,1] => 1260 [4,2,2,2] => 978 [4,2,2,1,1] => 1896 [4,2,1,1,1,1] => 3780 [4,1,1,1,1,1,1] => 7560 [3,3,3,1] => 840 [3,3,2,2] => 1272 [3,3,2,1,1] => 2520 [3,3,1,1,1,1] => 5040 [3,2,2,2,1] => 3792 [3,2,2,1,1,1] => 7560 [3,2,1,1,1,1,1] => 15120 [3,1,1,1,1,1,1,1] => 30240 [2,2,2,2,2] => 5736 [2,2,2,2,1,1] => 11352 [2,2,2,1,1,1,1] => 22680 [2,2,1,1,1,1,1,1] => 45360 [2,1,1,1,1,1,1,1,1] => 90720 [1,1,1,1,1,1,1,1,1,1] => 181440 [11] => 1 [10,1] => 1 [9,2] => 5 [9,1,1] => 5 [8,3] => 10 [8,2,1] => 25 [8,1,1,1] => 45 [7,4] => 20 [7,3,1] => 60 [7,2,2] => 100 [7,2,1,1] => 180 [7,1,1,1,1] => 360 [6,5] => 26 [6,4,1] => 110 [6,3,2] => 220 [6,3,1,1] => 420 [6,2,2,1] => 640 [6,2,1,1,1] => 1260 [6,1,1,1,1,1] => 2520 [5,5,1] => 126 [5,4,2] => 330 [5,4,1,1] => 630 [5,3,3] => 420 [5,3,2,1] => 1260 [5,3,1,1,1] => 2520 [5,2,2,2] => 1920 [5,2,2,1,1] => 3780 [5,2,1,1,1,1] => 7560 [5,1,1,1,1,1,1] => 15120 [4,4,3] => 540 [4,4,2,1] => 1590 [4,4,1,1,1] => 3150 [4,3,3,1] => 2100 [4,3,2,2] => 3180 [4,3,2,1,1] => 6300 [4,3,1,1,1,1] => 12600 [4,2,2,2,1] => 9480 [4,2,2,1,1,1] => 18900 [4,2,1,1,1,1,1] => 37800 [4,1,1,1,1,1,1,1] => 75600 [3,3,3,2] => 4200 [3,3,3,1,1] => 8400 [3,3,2,2,1] => 12600 [3,3,2,1,1,1] => 25200 [3,3,1,1,1,1,1] => 50400 [3,2,2,2,2] => 18960 [3,2,2,2,1,1] => 37800 [3,2,2,1,1,1,1] => 75600 [3,2,1,1,1,1,1,1] => 151200 [3,1,1,1,1,1,1,1,1] => 302400 [2,2,2,2,2,1] => 56760 [2,2,2,2,1,1,1] => 113400 [2,2,2,1,1,1,1,1] => 226800 [2,2,1,1,1,1,1,1,1] => 453600 [2,1,1,1,1,1,1,1,1,1] => 907200 [1,1,1,1,1,1,1,1,1,1,1] => 1814400 [12] => 1 [11,1] => 1 [10,2] => 6 [10,1,1] => 6 [9,3] => 12 [9,2,1] => 30 [9,1,1,1] => 55 [8,4] => 29 [8,3,1] => 85 [8,2,2] => 140 [8,2,1,1] => 250 [8,1,1,1,1] => 495 [7,5] => 38 [7,4,1] => 170 [7,3,2] => 340 [7,3,1,1] => 660 [7,2,2,1] => 1000 [7,2,1,1,1] => 1980 [7,1,1,1,1,1] => 3960 [6,6] => 50 [6,5,1] => 236 [6,4,2] => 610 [6,4,1,1] => 1160 [6,3,3] => 781 [6,3,2,1] => 2320 [6,3,1,1,1] => 4620 [6,2,2,2] => 3530 [6,2,2,1,1] => 6940 [6,2,1,1,1,1] => 13860 [6,1,1,1,1,1,1] => 27720 [5,5,2] => 708 [5,5,1,1] => 1386 [5,4,3] => 1170 [5,4,2,1] => 3480 [5,4,1,1,1] => 6930 [5,3,3,1] => 4620 [5,3,2,2] => 6960 [5,3,2,1,1] => 13860 [5,3,1,1,1,1] => 27720 [5,2,2,2,1] => 20820 [5,2,2,1,1,1] => 41580 [5,2,1,1,1,1,1] => 83160 [5,1,1,1,1,1,1,1] => 166320 [4,4,4] => 1493 [4,4,3,1] => 5790 [4,4,2,2] => 8760 [4,4,2,1,1] => 17340 [4,4,1,1,1,1] => 34650 [4,3,3,2] => 11580 [4,3,3,1,1] => 23100 [4,3,2,2,1] => 34680 [4,3,2,1,1,1] => 69300 [4,3,1,1,1,1,1] => 138600 [4,2,2,2,2] => 52170 [4,2,2,2,1,1] => 103980 [4,2,2,1,1,1,1] => 207900 [4,2,1,1,1,1,1,1] => 415800 [4,1,1,1,1,1,1,1,1] => 831600 [3,3,3,3] => 15402 [3,3,3,2,1] => 46200 [3,3,3,1,1,1] => 92400 [3,3,2,2,2] => 69360 [3,3,2,2,1,1] => 138600 [3,3,2,1,1,1,1] => 277200 [3,3,1,1,1,1,1,1] => 554400 [3,2,2,2,2,1] => 207960 [3,2,2,2,1,1,1] => 415800 [3,2,2,1,1,1,1,1] => 831600 [3,2,1,1,1,1,1,1,1] => 1663200 [3,1,1,1,1,1,1,1,1,1] => 3326400 [2,2,2,2,2,2] => 312240 [2,2,2,2,2,1,1] => 623760 [2,2,2,2,1,1,1,1] => 1247400 [2,2,2,1,1,1,1,1,1] => 2494800 [2,2,1,1,1,1,1,1,1,1] => 4989600 [2,1,1,1,1,1,1,1,1,1,1] => 9979200 [1,1,1,1,1,1,1,1,1,1,1,1] => 19958400 [13] => 1 [12,1] => 1 [11,2] => 6 [11,1,1] => 6 [10,3] => 14 [10,2,1] => 36 [10,1,1,1] => 66 [9,4] => 35 [9,3,1] => 110 [9,2,2] => 180 [9,2,1,1] => 330 [9,1,1,1,1] => 660 [8,5] => 57 [8,4,1] => 255 [8,3,2] => 510 [8,3,1,1] => 990 [8,2,2,1] => 1500 [8,2,1,1,1] => 2970 [8,1,1,1,1,1] => 5940 [7,6] => 76 [7,5,1] => 396 [7,4,2] => 1020 [7,4,1,1] => 1980 [7,3,3] => 1320 [7,3,2,1] => 3960 [7,3,1,1,1] => 7920 [7,2,2,2] => 6000 [7,2,2,1,1] => 11880 [7,2,1,1,1,1] => 23760 [7,1,1,1,1,1,1] => 47520 [6,6,1] => 472 [6,5,2] => 1416 [6,5,1,1] => 2772 [6,4,3] => 2340 [6,4,2,1] => 6960 [6,4,1,1,1] => 13860 [6,3,3,1] => 9240 [6,3,2,2] => 13920 [6,3,2,1,1] => 27720 [6,3,1,1,1,1] => 55440 [6,2,2,2,1] => 41640 [6,2,2,1,1,1] => 83160 [6,2,1,1,1,1,1] => 166320 [6,1,1,1,1,1,1,1] => 332640 [5,5,3] => 2772 [5,5,2,1] => 8316 [5,5,1,1,1] => 16632 [5,4,4] => 3510 [5,4,3,1] => 13860 [5,4,2,2] => 20880 [5,4,2,1,1] => 41580 [5,4,1,1,1,1] => 83160 [5,3,3,2] => 27720 [5,3,3,1,1] => 55440 [5,3,2,2,1] => 83160 [5,3,2,1,1,1] => 166320 [5,3,1,1,1,1,1] => 332640 [5,2,2,2,2] => 124920 [5,2,2,2,1,1] => 249480 [5,2,2,1,1,1,1] => 498960 [5,2,1,1,1,1,1,1] => 997920 [5,1,1,1,1,1,1,1,1] => 1995840 [4,4,4,1] => 17370 [4,4,3,2] => 34740 [4,4,3,1,1] => 69300 [4,4,2,2,1] => 104040 [4,4,2,1,1,1] => 207900 [4,4,1,1,1,1,1] => 415800 [4,3,3,3] => 46200 [4,3,3,2,1] => 138600 [4,3,3,1,1,1] => 277200 [4,3,2,2,2] => 208080 [4,3,2,2,1,1] => 415800 [4,3,2,1,1,1,1] => 831600 [4,3,1,1,1,1,1,1] => 1663200 [4,2,2,2,2,1] => 623880 [4,2,2,2,1,1,1] => 1247400 [4,2,2,1,1,1,1,1] => 2494800 [4,2,1,1,1,1,1,1,1] => 4989600 [4,1,1,1,1,1,1,1,1,1] => 9979200 [3,3,3,3,1] => 184800 [3,3,3,2,2] => 277200 [3,3,3,2,1,1] => 554400 [3,3,3,1,1,1,1] => 1108800 [3,3,2,2,2,1] => 831600 [3,3,2,2,1,1,1] => 1663200 [3,3,2,1,1,1,1,1] => 3326400 [3,3,1,1,1,1,1,1,1] => 6652800 [3,2,2,2,2,2] => 1247760 [3,2,2,2,2,1,1] => 2494800 [3,2,2,2,1,1,1,1] => 4989600 [3,2,2,1,1,1,1,1,1] => 9979200 [3,2,1,1,1,1,1,1,1,1] => 19958400 [3,1,1,1,1,1,1,1,1,1,1] => 39916800 [2,2,2,2,2,2,1] => 3742560 [2,2,2,2,2,1,1,1] => 7484400 [2,2,2,2,1,1,1,1,1] => 14968800 [2,2,2,1,1,1,1,1,1,1] => 29937600 [2,2,1,1,1,1,1,1,1,1,1] => 59875200 [2,1,1,1,1,1,1,1,1,1,1,1] => 119750400 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 239500800 [14] => 1 [13,1] => 1 [12,2] => 7 [12,1,1] => 7 [11,3] => 16 [11,2,1] => 42 [11,1,1,1] => 78 [10,4] => 47 [10,3,1] => 146 [10,2,2] => 237 [10,2,1,1] => 432 [10,1,1,1,1] => 858 [9,5] => 79 [9,4,1] => 365 [9,3,2] => 730 [9,3,1,1] => 1430 [9,2,2,1] => 2160 [9,2,1,1,1] => 4290 [9,1,1,1,1,1] => 8580 [8,6] => 126 [8,5,1] => 651 [8,4,2] => 1665 [8,4,1,1] => 3225 [8,3,3] => 2160 [8,3,2,1] => 6450 [8,3,1,1,1] => 12870 [8,2,2,2] => 9765 [8,2,2,1,1] => 19320 [8,2,1,1,1,1] => 38610 [8,1,1,1,1,1,1] => 77220 [7,7] => 133 [7,6,1] => 868 [7,5,2] => 2604 [7,5,1,1] => 5148 [7,4,3] => 4320 [7,4,2,1] => 12900 [7,4,1,1,1] => 25740 [7,3,3,1] => 17160 [7,3,2,2] => 25800 [7,3,2,1,1] => 51480 [7,3,1,1,1,1] => 102960 [7,2,2,2,1] => 77280 [7,2,2,1,1,1] => 154440 [7,2,1,1,1,1,1] => 308880 [7,1,1,1,1,1,1,1] => 617760 [6,6,2] => 3078 [6,6,1,1] => 6016 [6,5,3] => 6036 [6,5,2,1] => 18048 [6,5,1,1,1] => 36036 [6,4,4] => 7620 [6,4,3,1] => 30060 [6,4,2,2] => 45270 [6,4,2,1,1] => 90120 [6,4,1,1,1,1] => 180180 [6,3,3,2] => 60120 [6,3,3,1,1] => 120120 [6,3,2,2,1] => 180240 [6,3,2,1,1,1] => 360360 [6,3,1,1,1,1,1] => 720720 [6,2,2,2,2] => 270720 [6,2,2,2,1,1] => 540600 [6,2,2,1,1,1,1] => 1081080 [6,2,1,1,1,1,1,1] => 2162160 [6,1,1,1,1,1,1,1,1] => 4324320 [5,5,4] => 9054 [5,5,3,1] => 36036 [5,5,2,2] => 54144 [5,5,2,1,1] => 108108 [5,5,1,1,1,1] => 216216 [5,4,4,1] => 45090 [5,4,3,2] => 90180 [5,4,3,1,1] => 180180 [5,4,2,2,1] => 270360 [5,4,2,1,1,1] => 540540 [5,4,1,1,1,1,1] => 1081080 [5,3,3,3] => 120120 [5,3,3,2,1] => 360360 [5,3,3,1,1,1] => 720720 [5,3,2,2,2] => 540720 [5,3,2,2,1,1] => 1081080 [5,3,2,1,1,1,1] => 2162160 [5,3,1,1,1,1,1,1] => 4324320 [5,2,2,2,2,1] => 1621800 [5,2,2,2,1,1,1] => 3243240 [5,2,2,1,1,1,1,1] => 6486480 [5,2,1,1,1,1,1,1,1] => 12972960 [5,1,1,1,1,1,1,1,1,1] => 25945920 [4,4,4,2] => 112950 [4,4,4,1,1] => 225270 [4,4,3,3] => 150240 [4,4,3,2,1] => 450540 [4,4,3,1,1,1] => 900900 [4,4,2,2,2] => 676350 [4,4,2,2,1,1] => 1351440 [4,4,2,1,1,1,1] => 2702700 [4,4,1,1,1,1,1,1] => 5405400 [4,3,3,3,1] => 600600 [4,3,3,2,2] => 901080 [4,3,3,2,1,1] => 1801800 [4,3,3,1,1,1,1] => 3603600 [4,3,2,2,2,1] => 2702880 [4,3,2,2,1,1,1] => 5405400 [4,3,2,1,1,1,1,1] => 10810800 [4,3,1,1,1,1,1,1,1] => 21621600 [4,2,2,2,2,2] => 4055400 [4,2,2,2,2,1,1] => 8108280 [4,2,2,2,1,1,1,1] => 16216200 [4,2,2,1,1,1,1,1,1] => 32432400 [4,2,1,1,1,1,1,1,1,1] => 64864800 [4,1,1,1,1,1,1,1,1,1,1] => 129729600 [3,3,3,3,2] => 1201200 [3,3,3,3,1,1] => 2402400 [3,3,3,2,2,1] => 3603600 [3,3,3,2,1,1,1] => 7207200 [3,3,3,1,1,1,1,1] => 14414400 [3,3,2,2,2,2] => 5405760 [3,3,2,2,2,1,1] => 10810800 [3,3,2,2,1,1,1,1] => 21621600 [3,3,2,1,1,1,1,1,1] => 43243200 [3,3,1,1,1,1,1,1,1,1] => 86486400 [3,2,2,2,2,2,1] => 16216560 [3,2,2,2,2,1,1,1] => 32432400 [3,2,2,2,1,1,1,1,1] => 64864800 [3,2,2,1,1,1,1,1,1,1] => 129729600 [3,2,1,1,1,1,1,1,1,1,1] => 259459200 [3,1,1,1,1,1,1,1,1,1,1,1] => 518918400 [2,2,2,2,2,2,2] => 24327000 [2,2,2,2,2,2,1,1] => 48648960 [2,2,2,2,2,1,1,1,1] => 97297200 [2,2,2,2,1,1,1,1,1,1] => 194594400 [2,2,2,1,1,1,1,1,1,1,1] => 389188800 [2,2,1,1,1,1,1,1,1,1,1,1] => 778377600 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 1556755200 [15] => 1 [14,1] => 1 [13,2] => 7 [13,1,1] => 7 [12,3] => 19 [12,2,1] => 49 [12,1,1,1] => 91 [11,4] => 56 [11,3,1] => 182 [11,2,2] => 294 [11,2,1,1] => 546 [11,1,1,1,1] => 1092 [10,5] => 111 [10,4,1] => 511 [10,3,2] => 1022 [10,3,1,1] => 2002 [10,2,2,1] => 3024 [10,2,1,1,1] => 6006 [10,1,1,1,1,1] => 12012 [9,6] => 185 [9,5,1] => 1001 [9,4,2] => 2555 [9,4,1,1] => 5005 [9,3,3] => 3338 [9,3,2,1] => 10010 [9,3,1,1,1] => 20020 [9,2,2,2] => 15120 [9,2,2,1,1] => 30030 [9,2,1,1,1,1] => 60060 [9,1,1,1,1,1,1] => 120120 [8,7] => 232 [8,6,1] => 1519 [8,5,2] => 4557 [8,5,1,1] => 9009 [8,4,3] => 7560 [8,4,2,1] => 22575 [8,4,1,1,1] => 45045 [8,3,3,1] => 30030 [8,3,2,2] => 45150 [8,3,2,1,1] => 90090 [8,3,1,1,1,1] => 180180 [8,2,2,2,1] => 135240 [8,2,2,1,1,1] => 270270 [8,2,1,1,1,1,1] => 540540 [8,1,1,1,1,1,1,1] => 1081080 [7,7,1] => 1716 [7,6,2] => 6076 [7,6,1,1] => 12012 [7,5,3] => 12012 [7,5,2,1] => 36036 [7,5,1,1,1] => 72072 [7,4,4] => 15120 [7,4,3,1] => 60060 [7,4,2,2] => 90300 [7,4,2,1,1] => 180180 [7,4,1,1,1,1] => 360360 [7,3,3,2] => 120120 [7,3,3,1,1] => 240240 [7,3,2,2,1] => 360360 [7,3,2,1,1,1] => 720720 [7,3,1,1,1,1,1] => 1441440 [7,2,2,2,2] => 540960 [7,2,2,2,1,1] => 1081080 [7,2,2,1,1,1,1] => 2162160 [7,2,1,1,1,1,1,1] => 4324320 [7,1,1,1,1,1,1,1,1] => 8648640 [6,6,3] => 14086 [6,6,2,1] => 42112 [6,6,1,1,1] => 84084 [6,5,4] => 21126 [6,5,3,1] => 84084 [6,5,2,2] => 126336 [6,5,2,1,1] => 252252 [6,5,1,1,1,1] => 504504 [6,4,4,1] => 105210 [6,4,3,2] => 210420 [6,4,3,1,1] => 420420 [6,4,2,2,1] => 630840 [6,4,2,1,1,1] => 1261260 [6,4,1,1,1,1,1] => 2522520 [6,3,3,3] => 280284 [6,3,3,2,1] => 840840 [6,3,3,1,1,1] => 1681680 [6,3,2,2,2] => 1261680 [6,3,2,2,1,1] => 2522520 [6,3,2,1,1,1,1] => 5045040 [6,3,1,1,1,1,1,1] => 10090080 [6,2,2,2,2,1] => 3784200 [6,2,2,2,1,1,1] => 7567560 [6,2,2,1,1,1,1,1] => 15135120 [6,2,1,1,1,1,1,1,1] => 30270240 [6,1,1,1,1,1,1,1,1,1] => 60540480 [5,5,5] => 25226 [5,5,4,1] => 126126 [5,5,3,2] => 252252 [5,5,3,1,1] => 504504 [5,5,2,2,1] => 756756 [5,5,2,1,1,1] => 1513512 [5,5,1,1,1,1,1] => 3027024 [5,4,4,2] => 315630 [5,4,4,1,1] => 630630 [5,4,3,3] => 420420 [5,4,3,2,1] => 1261260 [5,4,3,1,1,1] => 2522520 [5,4,2,2,2] => 1892520 [5,4,2,2,1,1] => 3783780 [5,4,2,1,1,1,1] => 7567560 [5,4,1,1,1,1,1,1] => 15135120 [5,3,3,3,1] => 1681680 [5,3,3,2,2] => 2522520 [5,3,3,2,1,1] => 5045040 [5,3,3,1,1,1,1] => 10090080 [5,3,2,2,2,1] => 7567560 [5,3,2,2,1,1,1] => 15135120 [5,3,2,1,1,1,1,1] => 30270240 [5,3,1,1,1,1,1,1,1] => 60540480 [5,2,2,2,2,2] => 11352600 [5,2,2,2,2,1,1] => 22702680 [5,2,2,2,1,1,1,1] => 45405360 [5,2,2,1,1,1,1,1,1] => 90810720 [5,2,1,1,1,1,1,1,1,1] => 181621440 [5,1,1,1,1,1,1,1,1,1,1] => 363242880 [4,4,4,3] => 525840 [4,4,4,2,1] => 1576890 [4,4,4,1,1,1] => 3153150 [4,4,3,3,1] => 2102100 [4,4,3,2,2] => 3153780 [4,4,3,2,1,1] => 6306300 [4,4,3,1,1,1,1] => 12612600 [4,4,2,2,2,1] => 9460080 [4,4,2,2,1,1,1] => 18918900 [4,4,2,1,1,1,1,1] => 37837800 [4,4,1,1,1,1,1,1,1] => 75675600 [4,3,3,3,2] => 4204200 [4,3,3,3,1,1] => 8408400 [4,3,3,2,2,1] => 12612600 [4,3,3,2,1,1,1] => 25225200 [4,3,3,1,1,1,1,1] => 50450400 [4,3,2,2,2,2] => 18920160 [4,3,2,2,2,1,1] => 37837800 [4,3,2,2,1,1,1,1] => 75675600 [4,3,2,1,1,1,1,1,1] => 151351200 [4,3,1,1,1,1,1,1,1,1] => 302702400 [4,2,2,2,2,2,1] => 56757960 [4,2,2,2,2,1,1,1] => 113513400 [4,2,2,2,1,1,1,1,1] => 227026800 [4,2,2,1,1,1,1,1,1,1] => 454053600 [4,2,1,1,1,1,1,1,1,1,1] => 908107200 [4,1,1,1,1,1,1,1,1,1,1,1] => 1816214400 [3,3,3,3,3] => 5605608 [3,3,3,3,2,1] => 16816800 [3,3,3,3,1,1,1] => 33633600 [3,3,3,2,2,2] => 25225200 [3,3,3,2,2,1,1] => 50450400 [3,3,3,2,1,1,1,1] => 100900800 [3,3,3,1,1,1,1,1,1] => 201801600 [3,3,2,2,2,2,1] => 75675600 [3,3,2,2,2,1,1,1] => 151351200 [3,3,2,2,1,1,1,1,1] => 302702400 [3,3,2,1,1,1,1,1,1,1] => 605404800 [3,3,1,1,1,1,1,1,1,1,1] => 1210809600 [3,2,2,2,2,2,2] => 113515920 [3,2,2,2,2,2,1,1] => 227026800 [3,2,2,2,2,1,1,1,1] => 454053600 [3,2,2,2,1,1,1,1,1,1] => 908107200 [3,2,2,1,1,1,1,1,1,1,1] => 1816214400 [2,2,2,2,2,2,2,1] => 340542720 [2,2,2,2,2,2,1,1,1] => 681080400 [2,2,2,2,2,1,1,1,1,1] => 1362160800 [16] => 1 [15,1] => 1 [14,2] => 8 [14,1,1] => 8 [13,3] => 21 [13,2,1] => 56 [13,1,1,1] => 105 [12,4] => 72 [12,3,1] => 231 [12,2,2] => 371 [12,2,1,1] => 686 [12,1,1,1,1] => 1365 [11,5] => 147 [11,4,1] => 693 [11,3,2] => 1386 [11,3,1,1] => 2730 [11,2,2,1] => 4116 [11,2,1,1,1] => 8190 [11,1,1,1,1,1] => 16380 [10,6] => 280 [10,5,1] => 1512 [10,4,2] => 3843 [10,4,1,1] => 7518 [10,3,3] => 5026 [10,3,2,1] => 15036 [10,3,1,1,1] => 30030 [10,2,2,2] => 22701 [10,2,2,1,1] => 45066 [10,2,1,1,1,1] => 90090 [10,1,1,1,1,1,1] => 180180 [9,7] => 375 [9,6,1] => 2520 [9,5,2] => 7560 [9,5,1,1] => 15015 [9,4,3] => 12565 [9,4,2,1] => 37590 [9,4,1,1,1] => 75075 [9,3,3,1] => 50050 [9,3,2,2] => 75180 [9,3,2,1,1] => 150150 [9,3,1,1,1,1] => 300300 [9,2,2,2,1] => 225330 [9,2,2,1,1,1] => 450450 [9,2,1,1,1,1,1] => 900900 [9,1,1,1,1,1,1,1] => 1801800 [8,8] => 440 [8,7,1] => 3235 [8,6,2] => 11410 [8,6,1,1] => 22540 [8,5,3] => 22575 [8,5,2,1] => 67620 [8,5,1,1,1] => 135135 [8,4,4] => 28377 [8,4,3,1] => 112665 [8,4,2,2] => 169365 [8,4,2,1,1] => 337890 [8,4,1,1,1,1] => 675675 [8,3,3,2] => 225330 [8,3,3,1,1] => 450450 [8,3,2,2,1] => 675780 [8,3,2,1,1,1] => 1351350 [8,3,1,1,1,1,1] => 2702700 [8,2,2,2,2] => 1014405 [8,2,2,2,1,1] => 2027130 [8,2,2,1,1,1,1] => 4054050 [8,2,1,1,1,1,1,1] => 8108100 [8,1,1,1,1,1,1,1,1] => 16216200 [7,7,2] => 12940 [7,7,1,1] => 25740 [7,6,3] => 30100 [7,6,2,1] => 90160 [7,6,1,1,1] => 180180 [7,5,4] => 45150 [7,5,3,1] => 180180 [7,5,2,2] => 270480 [7,5,2,1,1] => 540540 [7,5,1,1,1,1] => 1081080 [7,4,4,1] => 225330 [7,4,3,2] => 450660 [7,4,3,1,1] => 900900 [7,4,2,2,1] => 1351560 [7,4,2,1,1,1] => 2702700 [7,4,1,1,1,1,1] => 5405400 [7,3,3,3] => 600600 [7,3,3,2,1] => 1801800 [7,3,3,1,1,1] => 3603600 [7,3,2,2,2] => 2703120 [7,3,2,2,1,1] => 5405400 [7,3,2,1,1,1,1] => 10810800 [7,3,1,1,1,1,1,1] => 21621600 [7,2,2,2,2,1] => 8108520 [7,2,2,2,1,1,1] => 16216200 [7,2,2,1,1,1,1,1] => 32432400 [7,2,1,1,1,1,1,1,1] => 64864800 [7,1,1,1,1,1,1,1,1,1] => 129729600 [6,6,4] => 52850 [6,6,3,1] => 210280 [6,6,2,2] => 315910 [6,6,2,1,1] => 630700 [6,6,1,1,1,1] => 1261260 [6,5,5] => 63168 [6,5,4,1] => 315420 [6,5,3,2] => 630840 [6,5,3,1,1] => 1261260 [6,5,2,2,1] => 1892100 [6,5,2,1,1,1] => 3783780 [6,5,1,1,1,1,1] => 7567560 [6,4,4,2] => 789180 [6,4,4,1,1] => 1576680 [6,4,3,3] => 1051260 [6,4,3,2,1] => 3153360 [6,4,3,1,1,1] => 6306300 [6,4,2,2,2] => 4731510 [6,4,2,2,1,1] => 9459660 [6,4,2,1,1,1,1] => 18918900 [6,4,1,1,1,1,1,1] => 37837800 [6,3,3,3,1] => 4204200 [6,3,3,2,2] => 6306720 [6,3,3,2,1,1] => 12612600 [6,3,3,1,1,1,1] => 25225200 [6,3,2,2,2,1] => 18919320 [6,3,2,2,1,1,1] => 37837800 [6,3,2,1,1,1,1,1] => 75675600 [6,3,1,1,1,1,1,1,1] => 151351200 [6,2,2,2,2,2] => 28381920 [6,2,2,2,2,1,1] => 56757120 [6,2,2,2,1,1,1,1] => 113513400 [6,2,2,1,1,1,1,1,1] => 227026800 [6,2,1,1,1,1,1,1,1,1] => 454053600 [6,1,1,1,1,1,1,1,1,1,1] => 908107200 [5,5,5,1] => 378378 [5,5,4,2] => 946260 [5,5,4,1,1] => 1891890 [5,5,3,3] => 1261260 [5,5,3,2,1] => 3783780 [5,5,3,1,1,1] => 7567560 [5,5,2,2,2] => 5676300 [5,5,2,2,1,1] => 11351340 [5,5,2,1,1,1,1] => 22702680 [5,5,1,1,1,1,1,1] => 45405360 [5,4,4,3] => 1576890 [5,4,4,2,1] => 4730040 [5,4,4,1,1,1] => 9459450 [5,4,3,3,1] => 6306300 [5,4,3,2,2] => 9460080 [5,4,3,2,1,1] => 18918900 [5,4,3,1,1,1,1] => 37837800 [5,4,2,2,2,1] => 28378980 [5,4,2,2,1,1,1] => 56756700 [5,4,2,1,1,1,1,1] => 113513400 [5,4,1,1,1,1,1,1,1] => 227026800 [5,3,3,3,2] => 12612600 [5,3,3,3,1,1] => 25225200 [5,3,3,2,2,1] => 37837800 [5,3,3,2,1,1,1] => 75675600 [5,3,3,1,1,1,1,1] => 151351200 [5,3,2,2,2,2] => 56757960 [5,3,2,2,2,1,1] => 113513400 [5,3,2,2,1,1,1,1] => 227026800 [5,3,2,1,1,1,1,1,1] => 454053600 [5,3,1,1,1,1,1,1,1,1] => 908107200 [5,2,2,2,2,2,1] => 170271360 [5,2,2,2,2,1,1,1] => 340540200 [5,2,2,2,1,1,1,1,1] => 681080400 [5,2,2,1,1,1,1,1,1,1] => 1362160800 [4,4,4,4] => 1972059 [4,4,4,3,1] => 7883190 [4,4,4,2,2] => 11826990 [4,4,4,2,1,1] => 23648940 [4,4,4,1,1,1,1] => 47297250 [4,4,3,3,2] => 15766380 [4,4,3,3,1,1] => 31531500 [4,4,3,2,2,1] => 47297880 [4,4,3,2,1,1,1] => 94594500 [4,4,3,1,1,1,1,1] => 189189000 [4,4,2,2,2,2] => 70951230 [4,4,2,2,2,1,1] => 141892380 [4,4,2,2,1,1,1,1] => 283783500 [4,4,2,1,1,1,1,1,1] => 567567000 [4,4,1,1,1,1,1,1,1,1] => 1135134000 [4,3,3,3,3] => 21021000 [4,3,3,3,2,1] => 63063000 [4,3,3,3,1,1,1] => 126126000 [4,3,3,2,2,2] => 94595760 [4,3,3,2,2,1,1] => 189189000 [4,3,3,2,1,1,1,1] => 378378000 [4,3,3,1,1,1,1,1,1] => 756756000 [4,3,2,2,2,2,1] => 283784760 [4,3,2,2,2,1,1,1] => 567567000 [4,3,2,2,1,1,1,1,1] => 1135134000 [4,2,2,2,2,2,2] => 425685960 [4,2,2,2,2,2,1,1] => 851351760 [4,2,2,2,2,1,1,1,1] => 1702701000 [3,3,3,3,3,1] => 84084000 [3,3,3,3,2,2] => 126126000 [3,3,3,3,2,1,1] => 252252000 [3,3,3,3,1,1,1,1] => 504504000 [3,3,3,2,2,2,1] => 378378000 [3,3,3,2,2,1,1,1] => 756756000 [3,3,3,2,1,1,1,1,1] => 1513512000 [3,3,2,2,2,2,2] => 567569520 [3,3,2,2,2,2,1,1] => 1135134000 [3,2,2,2,2,2,2,1] => 1702703520 [17] => 1 [16,1] => 1 [15,2] => 8 [15,1,1] => 8 [14,3] => 24 [14,2,1] => 64 [14,1,1,1] => 120 [13,4] => 84 [13,3,1] => 280 [13,2,2] => 448 [13,2,1,1] => 840 [13,1,1,1,1] => 1680 [12,5] => 196 [12,4,1] => 924 [12,3,2] => 1848 [12,3,1,1] => 3640 [12,2,2,1] => 5488 [12,2,1,1,1] => 10920 [12,1,1,1,1,1] => 21840 [11,6] => 392 [11,5,1] => 2184 [11,4,2] => 5544 [11,4,1,1] => 10920 [11,3,3] => 7280 [11,3,2,1] => 21840 [11,3,1,1,1] => 43680 [11,2,2,2] => 32928 [11,2,2,1,1] => 65520 [11,2,1,1,1,1] => 131040 [11,1,1,1,1,1,1] => 262080 [10,7] => 600 [10,6,1] => 4032 [10,5,2] => 12096 [10,5,1,1] => 24024 [10,4,3] => 20104 [10,4,2,1] => 60144 [10,4,1,1,1] => 120120 [10,3,3,1] => 80080 [10,3,2,2] => 120288 [10,3,2,1,1] => 240240 [10,3,1,1,1,1] => 480480 [10,2,2,2,1] => 360528 [10,2,2,1,1,1] => 720720 [10,2,1,1,1,1,1] => 1441440 [10,1,1,1,1,1,1,1] => 2882880 [9,8] => 750 [9,7,1] => 5720 [9,6,2] => 20160 [9,6,1,1] => 40040 [9,5,3] => 40040 [9,5,2,1] => 120120 [9,5,1,1,1] => 240240 [9,4,4] => 50260 [9,4,3,1] => 200200 [9,4,2,2] => 300720 [9,4,2,1,1] => 600600 [9,4,1,1,1,1] => 1201200 [9,3,3,2] => 400400 [9,3,3,1,1] => 800800 [9,3,2,2,1] => 1201200 [9,3,2,1,1,1] => 2402400 [9,3,1,1,1,1,1] => 4804800 [9,2,2,2,2] => 1802640 [9,2,2,2,1,1] => 3603600 [9,2,2,1,1,1,1] => 7207200 [9,2,1,1,1,1,1,1] => 14414400 [9,1,1,1,1,1,1,1,1] => 28828800 [8,8,1] => 6470 [8,7,2] => 25880 [8,7,1,1] => 51480 [8,6,3] => 60200 [8,6,2,1] => 180320 [8,6,1,1,1] => 360360 [8,5,4] => 90300 [8,5,3,1] => 360360 [8,5,2,2] => 540960 [8,5,2,1,1] => 1081080 [8,5,1,1,1,1] => 2162160 [8,4,4,1] => 450660 [8,4,3,2] => 901320 [8,4,3,1,1] => 1801800 [8,4,2,2,1] => 2703120 [8,4,2,1,1,1] => 5405400 [8,4,1,1,1,1,1] => 10810800 [8,3,3,3] => 1201200 [8,3,3,2,1] => 3603600 [8,3,3,1,1,1] => 7207200 [8,3,2,2,2] => 5406240 [8,3,2,2,1,1] => 10810800 [8,3,2,1,1,1,1] => 21621600 [8,3,1,1,1,1,1,1] => 43243200 [8,2,2,2,2,1] => 16217040 [8,2,2,2,1,1,1] => 32432400 [8,2,2,1,1,1,1,1] => 64864800 [8,2,1,1,1,1,1,1,1] => 129729600 [8,1,1,1,1,1,1,1,1,1] => 259459200 [7,7,3] => 68640 [7,7,2,1] => 205920 [7,7,1,1,1] => 411840 [7,6,4] => 120400 [7,6,3,1] => 480480 [7,6,2,2] => 721280 [7,6,2,1,1] => 1441440 [7,6,1,1,1,1] => 2882880 [7,5,5] => 144144 [7,5,4,1] => 720720 [7,5,3,2] => 1441440 [7,5,3,1,1] => 2882880 [7,5,2,2,1] => 4324320 [7,5,2,1,1,1] => 8648640 [7,5,1,1,1,1,1] => 17297280 [7,4,4,2] => 1802640 [7,4,4,1,1] => 3603600 [7,4,3,3] => 2402400 [7,4,3,2,1] => 7207200 [7,4,3,1,1,1] => 14414400 [7,4,2,2,2] => 10812480 [7,4,2,2,1,1] => 21621600 [7,4,2,1,1,1,1] => 43243200 [7,4,1,1,1,1,1,1] => 86486400 [7,3,3,3,1] => 9609600 [7,3,3,2,2] => 14414400 [7,3,3,2,1,1] => 28828800 [7,3,3,1,1,1,1] => 57657600 [7,3,2,2,2,1] => 43243200 [7,3,2,2,1,1,1] => 86486400 [7,3,2,1,1,1,1,1] => 172972800 [7,3,1,1,1,1,1,1,1] => 345945600 [7,2,2,2,2,2] => 64868160 [7,2,2,2,2,1,1] => 129729600 [7,2,2,2,1,1,1,1] => 259459200 [7,2,2,1,1,1,1,1,1] => 518918400 [7,2,1,1,1,1,1,1,1,1] => 1037836800 [7,1,1,1,1,1,1,1,1,1,1] => 2075673600 [6,6,5] => 168448 [6,6,4,1] => 841120 [6,6,3,2] => 1682240 [6,6,3,1,1] => 3363360 [6,6,2,2,1] => 5045600 [6,6,2,1,1,1] => 10090080 [6,6,1,1,1,1,1] => 20180160 [6,5,5,1] => 1009008 [6,5,4,2] => 2523360 [6,5,4,1,1] => 5045040 [6,5,3,3] => 3363360 [6,5,3,2,1] => 10090080 [6,5,3,1,1,1] => 20180160 [6,5,2,2,2] => 15136800 [6,5,2,2,1,1] => 30270240 [6,5,2,1,1,1,1] => 60540480 [6,5,1,1,1,1,1,1] => 121080960 [6,4,4,3] => 4205040 [6,4,4,2,1] => 12613440 [6,4,4,1,1,1] => 25225200 [6,4,3,3,1] => 16816800 [6,4,3,2,2] => 25226880 [6,4,3,2,1,1] => 50450400 [6,4,3,1,1,1,1] => 100900800 [6,4,2,2,2,1] => 75677280 [6,4,2,2,1,1,1] => 151351200 [6,4,2,1,1,1,1,1] => 302702400 [6,4,1,1,1,1,1,1,1] => 605404800 [6,3,3,3,2] => 33633600 [6,3,3,3,1,1] => 67267200 [6,3,3,2,2,1] => 100900800 [6,3,3,2,1,1,1] => 201801600 [6,3,3,1,1,1,1,1] => 403603200 [6,3,2,2,2,2] => 151354560 [6,3,2,2,2,1,1] => 302702400 [6,3,2,2,1,1,1,1] => 605404800 [6,3,2,1,1,1,1,1,1] => 1210809600 [6,2,2,2,2,2,1] => 454056960 [6,2,2,2,2,1,1,1] => 908107200 [6,2,2,2,1,1,1,1,1] => 1816214400 [5,5,5,2] => 3027024 [5,5,5,1,1] => 6054048 [5,5,4,3] => 5045040 [5,5,4,2,1] => 15135120 [5,5,4,1,1,1] => 30270240 [5,5,3,3,1] => 20180160 [5,5,3,2,2] => 30270240 [5,5,3,2,1,1] => 60540480 [5,5,3,1,1,1,1] => 121080960 [5,5,2,2,2,1] => 90810720 [5,5,2,2,1,1,1] => 181621440 [5,5,2,1,1,1,1,1] => 363242880 [5,5,1,1,1,1,1,1,1] => 726485760 [5,4,4,4] => 6307560 [5,4,4,3,1] => 25225200 [5,4,4,2,2] => 37840320 [5,4,4,2,1,1] => 75675600 [5,4,4,1,1,1,1] => 151351200 [5,4,3,3,2] => 50450400 [5,4,3,3,1,1] => 100900800 [5,4,3,2,2,1] => 151351200 [5,4,3,2,1,1,1] => 302702400 [5,4,3,1,1,1,1,1] => 605404800 [5,4,2,2,2,2] => 227031840 [5,4,2,2,2,1,1] => 454053600 [5,4,2,2,1,1,1,1] => 908107200 [5,4,2,1,1,1,1,1,1] => 1816214400 [5,3,3,3,3] => 67267200 [5,3,3,3,2,1] => 201801600 [5,3,3,3,1,1,1] => 403603200 [5,3,3,2,2,2] => 302702400 [5,3,3,2,2,1,1] => 605404800 [5,3,3,2,1,1,1,1] => 1210809600 [5,3,2,2,2,2,1] => 908107200 [5,3,2,2,2,1,1,1] => 1816214400 [5,2,2,2,2,2,2] => 1362170880 [4,4,4,4,1] => 31532760 [4,4,4,3,2] => 63065520 [4,4,4,3,1,1] => 126126000 [4,4,4,2,2,1] => 189191520 [4,4,4,2,1,1,1] => 378378000 [4,4,4,1,1,1,1,1] => 756756000 [4,4,3,3,3] => 84084000 [4,4,3,3,2,1] => 252252000 [4,4,3,3,1,1,1] => 504504000 [4,4,3,2,2,2] => 378383040 [4,4,3,2,2,1,1] => 756756000 [4,4,3,2,1,1,1,1] => 1513512000 [4,4,2,2,2,2,1] => 1135139040 [4,3,3,3,3,1] => 336336000 [4,3,3,3,2,2] => 504504000 [4,3,3,3,2,1,1] => 1009008000 [4,3,3,3,1,1,1,1] => 2018016000 [4,3,3,2,2,2,1] => 1513512000 [3,3,3,3,3,2] => 672672000 [3,3,3,3,3,1,1] => 1345344000 [3,3,3,3,2,2,1] => 2018016000 ----------------------------------------------------------------------------- Created: Sep 27, 2020 at 11:53 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 27, 2020 at 11:53 by Martin Rubey