***************************************************************************** * 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: St001541 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The Gini index of an integer partition. As discussed in [1], this statistic is equal to [[St000567]] applied to the conjugate partition. ----------------------------------------------------------------------------- References: [1] Kopitzke, G. The Gini Index of an Integer Partition [[arXiv:2005.04284]] ----------------------------------------------------------------------------- Code: def statistic(L): L = L.conjugate() n = sum(L) return binomial(n+1,2) - sum(binomial(l+1,2) for l in L) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [2] => 1 [1,1] => 0 [3] => 3 [2,1] => 2 [1,1,1] => 0 [4] => 6 [3,1] => 5 [2,2] => 4 [2,1,1] => 3 [1,1,1,1] => 0 [5] => 10 [4,1] => 9 [3,2] => 8 [3,1,1] => 7 [2,2,1] => 6 [2,1,1,1] => 4 [1,1,1,1,1] => 0 [6] => 15 [5,1] => 14 [4,2] => 13 [4,1,1] => 12 [3,3] => 12 [3,2,1] => 11 [3,1,1,1] => 9 [2,2,2] => 9 [2,2,1,1] => 8 [2,1,1,1,1] => 5 [1,1,1,1,1,1] => 0 [7] => 21 [6,1] => 20 [5,2] => 19 [5,1,1] => 18 [4,3] => 18 [4,2,1] => 17 [4,1,1,1] => 15 [3,3,1] => 16 [3,2,2] => 15 [3,2,1,1] => 14 [3,1,1,1,1] => 11 [2,2,2,1] => 12 [2,2,1,1,1] => 10 [2,1,1,1,1,1] => 6 [1,1,1,1,1,1,1] => 0 [8] => 28 [7,1] => 27 [6,2] => 26 [6,1,1] => 25 [5,3] => 25 [5,2,1] => 24 [5,1,1,1] => 22 [4,4] => 24 [4,3,1] => 23 [4,2,2] => 22 [4,2,1,1] => 21 [4,1,1,1,1] => 18 [3,3,2] => 21 [3,3,1,1] => 20 [3,2,2,1] => 19 [3,2,1,1,1] => 17 [3,1,1,1,1,1] => 13 [2,2,2,2] => 16 [2,2,2,1,1] => 15 [2,2,1,1,1,1] => 12 [2,1,1,1,1,1,1] => 7 [1,1,1,1,1,1,1,1] => 0 [9] => 36 [8,1] => 35 [7,2] => 34 [7,1,1] => 33 [6,3] => 33 [6,2,1] => 32 [6,1,1,1] => 30 [5,4] => 32 [5,3,1] => 31 [5,2,2] => 30 [5,2,1,1] => 29 [5,1,1,1,1] => 26 [4,4,1] => 30 [4,3,2] => 29 [4,3,1,1] => 28 [4,2,2,1] => 27 [4,2,1,1,1] => 25 [4,1,1,1,1,1] => 21 [3,3,3] => 27 [3,3,2,1] => 26 [3,3,1,1,1] => 24 [3,2,2,2] => 24 [3,2,2,1,1] => 23 [3,2,1,1,1,1] => 20 [3,1,1,1,1,1,1] => 15 [2,2,2,2,1] => 20 [2,2,2,1,1,1] => 18 [2,2,1,1,1,1,1] => 14 [2,1,1,1,1,1,1,1] => 8 [1,1,1,1,1,1,1,1,1] => 0 [10] => 45 [9,1] => 44 [8,2] => 43 [8,1,1] => 42 [7,3] => 42 [7,2,1] => 41 [7,1,1,1] => 39 [6,4] => 41 [6,3,1] => 40 [6,2,2] => 39 [6,2,1,1] => 38 [6,1,1,1,1] => 35 [5,5] => 40 [5,4,1] => 39 [5,3,2] => 38 [5,3,1,1] => 37 [5,2,2,1] => 36 [5,2,1,1,1] => 34 [5,1,1,1,1,1] => 30 [4,4,2] => 37 [4,4,1,1] => 36 [4,3,3] => 36 [4,3,2,1] => 35 [4,3,1,1,1] => 33 [4,2,2,2] => 33 [4,2,2,1,1] => 32 [4,2,1,1,1,1] => 29 [4,1,1,1,1,1,1] => 24 [3,3,3,1] => 33 [3,3,2,2] => 32 [3,3,2,1,1] => 31 [3,3,1,1,1,1] => 28 [3,2,2,2,1] => 29 [3,2,2,1,1,1] => 27 [3,2,1,1,1,1,1] => 23 [3,1,1,1,1,1,1,1] => 17 [2,2,2,2,2] => 25 [2,2,2,2,1,1] => 24 [2,2,2,1,1,1,1] => 21 [2,2,1,1,1,1,1,1] => 16 [2,1,1,1,1,1,1,1,1] => 9 [1,1,1,1,1,1,1,1,1,1] => 0 [11] => 55 [10,1] => 54 [9,2] => 53 [9,1,1] => 52 [8,3] => 52 [8,2,1] => 51 [8,1,1,1] => 49 [7,4] => 51 [7,3,1] => 50 [7,2,2] => 49 [7,2,1,1] => 48 [7,1,1,1,1] => 45 [6,5] => 50 [6,4,1] => 49 [6,3,2] => 48 [6,3,1,1] => 47 [6,2,2,1] => 46 [6,2,1,1,1] => 44 [6,1,1,1,1,1] => 40 [5,5,1] => 48 [5,4,2] => 47 [5,4,1,1] => 46 [5,3,3] => 46 [5,3,2,1] => 45 [5,3,1,1,1] => 43 [5,2,2,2] => 43 [5,2,2,1,1] => 42 [5,2,1,1,1,1] => 39 [5,1,1,1,1,1,1] => 34 [4,4,3] => 45 [4,4,2,1] => 44 [4,4,1,1,1] => 42 [4,3,3,1] => 43 [4,3,2,2] => 42 [4,3,2,1,1] => 41 [4,3,1,1,1,1] => 38 [4,2,2,2,1] => 39 [4,2,2,1,1,1] => 37 [4,2,1,1,1,1,1] => 33 [4,1,1,1,1,1,1,1] => 27 [3,3,3,2] => 40 [3,3,3,1,1] => 39 [3,3,2,2,1] => 38 [3,3,2,1,1,1] => 36 [3,3,1,1,1,1,1] => 32 [3,2,2,2,2] => 35 [3,2,2,2,1,1] => 34 [3,2,2,1,1,1,1] => 31 [3,2,1,1,1,1,1,1] => 26 [3,1,1,1,1,1,1,1,1] => 19 [2,2,2,2,2,1] => 30 [2,2,2,2,1,1,1] => 28 [2,2,2,1,1,1,1,1] => 24 [2,2,1,1,1,1,1,1,1] => 18 [2,1,1,1,1,1,1,1,1,1] => 10 [1,1,1,1,1,1,1,1,1,1,1] => 0 [12] => 66 [11,1] => 65 [10,2] => 64 [10,1,1] => 63 [9,3] => 63 [9,2,1] => 62 [9,1,1,1] => 60 [8,4] => 62 [8,3,1] => 61 [8,2,2] => 60 [8,2,1,1] => 59 [8,1,1,1,1] => 56 [7,5] => 61 [7,4,1] => 60 [7,3,2] => 59 [7,3,1,1] => 58 [7,2,2,1] => 57 [7,2,1,1,1] => 55 [7,1,1,1,1,1] => 51 [6,6] => 60 [6,5,1] => 59 [6,4,2] => 58 [6,4,1,1] => 57 [6,3,3] => 57 [6,3,2,1] => 56 [6,3,1,1,1] => 54 [6,2,2,2] => 54 [6,2,2,1,1] => 53 [6,2,1,1,1,1] => 50 [6,1,1,1,1,1,1] => 45 [5,5,2] => 57 [5,5,1,1] => 56 [5,4,3] => 56 [5,4,2,1] => 55 [5,4,1,1,1] => 53 [5,3,3,1] => 54 [5,3,2,2] => 53 [5,3,2,1,1] => 52 [5,3,1,1,1,1] => 49 [5,2,2,2,1] => 50 [5,2,2,1,1,1] => 48 [5,2,1,1,1,1,1] => 44 [5,1,1,1,1,1,1,1] => 38 [4,4,4] => 54 [4,4,3,1] => 53 [4,4,2,2] => 52 [4,4,2,1,1] => 51 [4,4,1,1,1,1] => 48 [4,3,3,2] => 51 [4,3,3,1,1] => 50 [4,3,2,2,1] => 49 [4,3,2,1,1,1] => 47 [4,3,1,1,1,1,1] => 43 [4,2,2,2,2] => 46 [4,2,2,2,1,1] => 45 [4,2,2,1,1,1,1] => 42 [4,2,1,1,1,1,1,1] => 37 [4,1,1,1,1,1,1,1,1] => 30 [3,3,3,3] => 48 [3,3,3,2,1] => 47 [3,3,3,1,1,1] => 45 [3,3,2,2,2] => 45 [3,3,2,2,1,1] => 44 [3,3,2,1,1,1,1] => 41 [3,3,1,1,1,1,1,1] => 36 [3,2,2,2,2,1] => 41 [3,2,2,2,1,1,1] => 39 [3,2,2,1,1,1,1,1] => 35 [3,2,1,1,1,1,1,1,1] => 29 [3,1,1,1,1,1,1,1,1,1] => 21 [2,2,2,2,2,2] => 36 [2,2,2,2,2,1,1] => 35 [2,2,2,2,1,1,1,1] => 32 [2,2,2,1,1,1,1,1,1] => 27 [2,2,1,1,1,1,1,1,1,1] => 20 [2,1,1,1,1,1,1,1,1,1,1] => 11 [1,1,1,1,1,1,1,1,1,1,1,1] => 0 [13] => 78 [12,1] => 77 [11,2] => 76 [11,1,1] => 75 [10,3] => 75 [10,2,1] => 74 [10,1,1,1] => 72 [9,4] => 74 [9,3,1] => 73 [9,2,2] => 72 [9,2,1,1] => 71 [9,1,1,1,1] => 68 [8,5] => 73 [8,4,1] => 72 [8,3,2] => 71 [8,3,1,1] => 70 [8,2,2,1] => 69 [8,2,1,1,1] => 67 [8,1,1,1,1,1] => 63 [7,6] => 72 [7,5,1] => 71 [7,4,2] => 70 [7,4,1,1] => 69 [7,3,3] => 69 [7,3,2,1] => 68 [7,3,1,1,1] => 66 [7,2,2,2] => 66 [7,2,2,1,1] => 65 [7,2,1,1,1,1] => 62 [7,1,1,1,1,1,1] => 57 [6,6,1] => 70 [6,5,2] => 69 [6,5,1,1] => 68 [6,4,3] => 68 [6,4,2,1] => 67 [6,4,1,1,1] => 65 [6,3,3,1] => 66 [6,3,2,2] => 65 [6,3,2,1,1] => 64 [6,3,1,1,1,1] => 61 [6,2,2,2,1] => 62 [6,2,2,1,1,1] => 60 [6,2,1,1,1,1,1] => 56 [6,1,1,1,1,1,1,1] => 50 [5,5,3] => 67 [5,5,2,1] => 66 [5,5,1,1,1] => 64 [5,4,4] => 66 [5,4,3,1] => 65 [5,4,2,2] => 64 [5,4,2,1,1] => 63 [5,4,1,1,1,1] => 60 [5,3,3,2] => 63 [5,3,3,1,1] => 62 [5,3,2,2,1] => 61 [5,3,2,1,1,1] => 59 [5,3,1,1,1,1,1] => 55 [5,2,2,2,2] => 58 [5,2,2,2,1,1] => 57 [5,2,2,1,1,1,1] => 54 [5,2,1,1,1,1,1,1] => 49 [5,1,1,1,1,1,1,1,1] => 42 [4,4,4,1] => 63 [4,4,3,2] => 62 [4,4,3,1,1] => 61 [4,4,2,2,1] => 60 [4,4,2,1,1,1] => 58 [4,4,1,1,1,1,1] => 54 [4,3,3,3] => 60 [4,3,3,2,1] => 59 [4,3,3,1,1,1] => 57 [4,3,2,2,2] => 57 [4,3,2,2,1,1] => 56 [4,3,2,1,1,1,1] => 53 [4,3,1,1,1,1,1,1] => 48 [4,2,2,2,2,1] => 53 [4,2,2,2,1,1,1] => 51 [4,2,2,1,1,1,1,1] => 47 [4,2,1,1,1,1,1,1,1] => 41 [4,1,1,1,1,1,1,1,1,1] => 33 [3,3,3,3,1] => 56 [3,3,3,2,2] => 55 [3,3,3,2,1,1] => 54 [3,3,3,1,1,1,1] => 51 [3,3,2,2,2,1] => 52 [3,3,2,2,1,1,1] => 50 [3,3,2,1,1,1,1,1] => 46 [3,3,1,1,1,1,1,1,1] => 40 [3,2,2,2,2,2] => 48 [3,2,2,2,2,1,1] => 47 [3,2,2,2,1,1,1,1] => 44 [3,2,2,1,1,1,1,1,1] => 39 [3,2,1,1,1,1,1,1,1,1] => 32 [3,1,1,1,1,1,1,1,1,1,1] => 23 [2,2,2,2,2,2,1] => 42 [2,2,2,2,2,1,1,1] => 40 [2,2,2,2,1,1,1,1,1] => 36 [2,2,2,1,1,1,1,1,1,1] => 30 [2,2,1,1,1,1,1,1,1,1,1] => 22 [2,1,1,1,1,1,1,1,1,1,1,1] => 12 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [14] => 91 [13,1] => 90 [12,2] => 89 [12,1,1] => 88 [11,3] => 88 [11,2,1] => 87 [11,1,1,1] => 85 [10,4] => 87 [10,3,1] => 86 [10,2,2] => 85 [10,2,1,1] => 84 [10,1,1,1,1] => 81 [9,5] => 86 [9,4,1] => 85 [9,3,2] => 84 [9,3,1,1] => 83 [9,2,2,1] => 82 [9,2,1,1,1] => 80 [9,1,1,1,1,1] => 76 [8,6] => 85 [8,5,1] => 84 [8,4,2] => 83 [8,4,1,1] => 82 [8,3,3] => 82 [8,3,2,1] => 81 [8,3,1,1,1] => 79 [8,2,2,2] => 79 [8,2,2,1,1] => 78 [8,2,1,1,1,1] => 75 [8,1,1,1,1,1,1] => 70 [7,7] => 84 [7,6,1] => 83 [7,5,2] => 82 [7,5,1,1] => 81 [7,4,3] => 81 [7,4,2,1] => 80 [7,4,1,1,1] => 78 [7,3,3,1] => 79 [7,3,2,2] => 78 [7,3,2,1,1] => 77 [7,3,1,1,1,1] => 74 [7,2,2,2,1] => 75 [7,2,2,1,1,1] => 73 [7,2,1,1,1,1,1] => 69 [7,1,1,1,1,1,1,1] => 63 [6,6,2] => 81 [6,6,1,1] => 80 [6,5,3] => 80 [6,5,2,1] => 79 [6,5,1,1,1] => 77 [6,4,4] => 79 [6,4,3,1] => 78 [6,4,2,2] => 77 [6,4,2,1,1] => 76 [6,4,1,1,1,1] => 73 [6,3,3,2] => 76 [6,3,3,1,1] => 75 [6,3,2,2,1] => 74 [6,3,2,1,1,1] => 72 [6,3,1,1,1,1,1] => 68 [6,2,2,2,2] => 71 [6,2,2,2,1,1] => 70 [6,2,2,1,1,1,1] => 67 [6,2,1,1,1,1,1,1] => 62 [6,1,1,1,1,1,1,1,1] => 55 [5,5,4] => 78 [5,5,3,1] => 77 [5,5,2,2] => 76 [5,5,2,1,1] => 75 [5,5,1,1,1,1] => 72 [5,4,4,1] => 76 [5,4,3,2] => 75 [5,4,3,1,1] => 74 [5,4,2,2,1] => 73 [5,4,2,1,1,1] => 71 [5,4,1,1,1,1,1] => 67 [5,3,3,3] => 73 [5,3,3,2,1] => 72 [5,3,3,1,1,1] => 70 [5,3,2,2,2] => 70 [5,3,2,2,1,1] => 69 [5,3,2,1,1,1,1] => 66 [5,3,1,1,1,1,1,1] => 61 [5,2,2,2,2,1] => 66 [5,2,2,2,1,1,1] => 64 [5,2,2,1,1,1,1,1] => 60 [5,2,1,1,1,1,1,1,1] => 54 [5,1,1,1,1,1,1,1,1,1] => 46 [4,4,4,2] => 73 [4,4,4,1,1] => 72 [4,4,3,3] => 72 [4,4,3,2,1] => 71 [4,4,3,1,1,1] => 69 [4,4,2,2,2] => 69 [4,4,2,2,1,1] => 68 [4,4,2,1,1,1,1] => 65 [4,4,1,1,1,1,1,1] => 60 [4,3,3,3,1] => 69 [4,3,3,2,2] => 68 [4,3,3,2,1,1] => 67 [4,3,3,1,1,1,1] => 64 [4,3,2,2,2,1] => 65 [4,3,2,2,1,1,1] => 63 [4,3,2,1,1,1,1,1] => 59 [4,3,1,1,1,1,1,1,1] => 53 [4,2,2,2,2,2] => 61 [4,2,2,2,2,1,1] => 60 [4,2,2,2,1,1,1,1] => 57 [4,2,2,1,1,1,1,1,1] => 52 [4,2,1,1,1,1,1,1,1,1] => 45 [4,1,1,1,1,1,1,1,1,1,1] => 36 [3,3,3,3,2] => 65 [3,3,3,3,1,1] => 64 [3,3,3,2,2,1] => 63 [3,3,3,2,1,1,1] => 61 [3,3,3,1,1,1,1,1] => 57 [3,3,2,2,2,2] => 60 [3,3,2,2,2,1,1] => 59 [3,3,2,2,1,1,1,1] => 56 [3,3,2,1,1,1,1,1,1] => 51 [3,3,1,1,1,1,1,1,1,1] => 44 [3,2,2,2,2,2,1] => 55 [3,2,2,2,2,1,1,1] => 53 [3,2,2,2,1,1,1,1,1] => 49 [3,2,2,1,1,1,1,1,1,1] => 43 [3,2,1,1,1,1,1,1,1,1,1] => 35 [3,1,1,1,1,1,1,1,1,1,1,1] => 25 [2,2,2,2,2,2,2] => 49 [2,2,2,2,2,2,1,1] => 48 [2,2,2,2,2,1,1,1,1] => 45 [2,2,2,2,1,1,1,1,1,1] => 40 [2,2,2,1,1,1,1,1,1,1,1] => 33 [2,2,1,1,1,1,1,1,1,1,1,1] => 24 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 13 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [15] => 105 [14,1] => 104 [13,2] => 103 [13,1,1] => 102 [12,3] => 102 [12,2,1] => 101 [12,1,1,1] => 99 [11,4] => 101 [11,3,1] => 100 [11,2,2] => 99 [11,2,1,1] => 98 [11,1,1,1,1] => 95 [10,5] => 100 [10,4,1] => 99 [10,3,2] => 98 [10,3,1,1] => 97 [10,2,2,1] => 96 [10,2,1,1,1] => 94 [10,1,1,1,1,1] => 90 [9,6] => 99 [9,5,1] => 98 [9,4,2] => 97 [9,4,1,1] => 96 [9,3,3] => 96 [9,3,2,1] => 95 [9,3,1,1,1] => 93 [9,2,2,2] => 93 [9,2,2,1,1] => 92 [9,2,1,1,1,1] => 89 [9,1,1,1,1,1,1] => 84 [8,7] => 98 [8,6,1] => 97 [8,5,2] => 96 [8,5,1,1] => 95 [8,4,3] => 95 [8,4,2,1] => 94 [8,4,1,1,1] => 92 [8,3,3,1] => 93 [8,3,2,2] => 92 [8,3,2,1,1] => 91 [8,3,1,1,1,1] => 88 [8,2,2,2,1] => 89 [8,2,2,1,1,1] => 87 [8,2,1,1,1,1,1] => 83 [8,1,1,1,1,1,1,1] => 77 [7,7,1] => 96 [7,6,2] => 95 [7,6,1,1] => 94 [7,5,3] => 94 [7,5,2,1] => 93 [7,5,1,1,1] => 91 [7,4,4] => 93 [7,4,3,1] => 92 [7,4,2,2] => 91 [7,4,2,1,1] => 90 [7,4,1,1,1,1] => 87 [7,3,3,2] => 90 [7,3,3,1,1] => 89 [7,3,2,2,1] => 88 [7,3,2,1,1,1] => 86 [7,3,1,1,1,1,1] => 82 [7,2,2,2,2] => 85 [7,2,2,2,1,1] => 84 [7,2,2,1,1,1,1] => 81 [7,2,1,1,1,1,1,1] => 76 [7,1,1,1,1,1,1,1,1] => 69 [6,6,3] => 93 [6,6,2,1] => 92 [6,6,1,1,1] => 90 [6,5,4] => 92 [6,5,3,1] => 91 [6,5,2,2] => 90 [6,5,2,1,1] => 89 [6,5,1,1,1,1] => 86 [6,4,4,1] => 90 [6,4,3,2] => 89 [6,4,3,1,1] => 88 [6,4,2,2,1] => 87 [6,4,2,1,1,1] => 85 [6,4,1,1,1,1,1] => 81 [6,3,3,3] => 87 [6,3,3,2,1] => 86 [6,3,3,1,1,1] => 84 [6,3,2,2,2] => 84 [6,3,2,2,1,1] => 83 [6,3,2,1,1,1,1] => 80 [6,3,1,1,1,1,1,1] => 75 [6,2,2,2,2,1] => 80 [6,2,2,2,1,1,1] => 78 [6,2,2,1,1,1,1,1] => 74 [6,2,1,1,1,1,1,1,1] => 68 [6,1,1,1,1,1,1,1,1,1] => 60 [5,5,5] => 90 [5,5,4,1] => 89 [5,5,3,2] => 88 [5,5,3,1,1] => 87 [5,5,2,2,1] => 86 [5,5,2,1,1,1] => 84 [5,5,1,1,1,1,1] => 80 [5,4,4,2] => 87 [5,4,4,1,1] => 86 [5,4,3,3] => 86 [5,4,3,2,1] => 85 [5,4,3,1,1,1] => 83 [5,4,2,2,2] => 83 [5,4,2,2,1,1] => 82 [5,4,2,1,1,1,1] => 79 [5,4,1,1,1,1,1,1] => 74 [5,3,3,3,1] => 83 [5,3,3,2,2] => 82 [5,3,3,2,1,1] => 81 [5,3,3,1,1,1,1] => 78 [5,3,2,2,2,1] => 79 [5,3,2,2,1,1,1] => 77 [5,3,2,1,1,1,1,1] => 73 [5,3,1,1,1,1,1,1,1] => 67 [5,2,2,2,2,2] => 75 [5,2,2,2,2,1,1] => 74 [5,2,2,2,1,1,1,1] => 71 [5,2,2,1,1,1,1,1,1] => 66 [5,2,1,1,1,1,1,1,1,1] => 59 [5,1,1,1,1,1,1,1,1,1,1] => 50 [4,4,4,3] => 84 [4,4,4,2,1] => 83 [4,4,4,1,1,1] => 81 [4,4,3,3,1] => 82 [4,4,3,2,2] => 81 [4,4,3,2,1,1] => 80 [4,4,3,1,1,1,1] => 77 [4,4,2,2,2,1] => 78 [4,4,2,2,1,1,1] => 76 [4,4,2,1,1,1,1,1] => 72 [4,4,1,1,1,1,1,1,1] => 66 [4,3,3,3,2] => 79 [4,3,3,3,1,1] => 78 [4,3,3,2,2,1] => 77 [4,3,3,2,1,1,1] => 75 [4,3,3,1,1,1,1,1] => 71 [4,3,2,2,2,2] => 74 [4,3,2,2,2,1,1] => 73 [4,3,2,2,1,1,1,1] => 70 [4,3,2,1,1,1,1,1,1] => 65 [4,3,1,1,1,1,1,1,1,1] => 58 [4,2,2,2,2,2,1] => 69 [4,2,2,2,2,1,1,1] => 67 [4,2,2,2,1,1,1,1,1] => 63 [4,2,2,1,1,1,1,1,1,1] => 57 [4,2,1,1,1,1,1,1,1,1,1] => 49 [4,1,1,1,1,1,1,1,1,1,1,1] => 39 [3,3,3,3,3] => 75 [3,3,3,3,2,1] => 74 [3,3,3,3,1,1,1] => 72 [3,3,3,2,2,2] => 72 [3,3,3,2,2,1,1] => 71 [3,3,3,2,1,1,1,1] => 68 [3,3,3,1,1,1,1,1,1] => 63 [3,3,2,2,2,2,1] => 68 [3,3,2,2,2,1,1,1] => 66 [3,3,2,2,1,1,1,1,1] => 62 [3,3,2,1,1,1,1,1,1,1] => 56 [3,3,1,1,1,1,1,1,1,1,1] => 48 [3,2,2,2,2,2,2] => 63 [3,2,2,2,2,2,1,1] => 62 [3,2,2,2,2,1,1,1,1] => 59 [3,2,2,2,1,1,1,1,1,1] => 54 [3,2,2,1,1,1,1,1,1,1,1] => 47 [3,2,1,1,1,1,1,1,1,1,1,1] => 38 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 27 [2,2,2,2,2,2,2,1] => 56 [2,2,2,2,2,2,1,1,1] => 54 [2,2,2,2,2,1,1,1,1,1] => 50 [2,2,2,2,1,1,1,1,1,1,1] => 44 [2,2,2,1,1,1,1,1,1,1,1,1] => 36 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 26 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 14 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [16] => 120 [15,1] => 119 [14,2] => 118 [14,1,1] => 117 [13,3] => 117 [13,2,1] => 116 [13,1,1,1] => 114 [12,4] => 116 [12,3,1] => 115 [12,2,2] => 114 [12,2,1,1] => 113 [12,1,1,1,1] => 110 [11,5] => 115 [11,4,1] => 114 [11,3,2] => 113 [11,3,1,1] => 112 [11,2,2,1] => 111 [11,2,1,1,1] => 109 [11,1,1,1,1,1] => 105 [10,6] => 114 [10,5,1] => 113 [10,4,2] => 112 [10,4,1,1] => 111 [10,3,3] => 111 [10,3,2,1] => 110 [10,3,1,1,1] => 108 [10,2,2,2] => 108 [10,2,2,1,1] => 107 [10,2,1,1,1,1] => 104 [10,1,1,1,1,1,1] => 99 [9,7] => 113 [9,6,1] => 112 [9,5,2] => 111 [9,5,1,1] => 110 [9,4,3] => 110 [9,4,2,1] => 109 [9,4,1,1,1] => 107 [9,3,3,1] => 108 [9,3,2,2] => 107 [9,3,2,1,1] => 106 [9,3,1,1,1,1] => 103 [9,2,2,2,1] => 104 [9,2,2,1,1,1] => 102 [9,2,1,1,1,1,1] => 98 [9,1,1,1,1,1,1,1] => 92 [8,8] => 112 [8,7,1] => 111 [8,6,2] => 110 [8,6,1,1] => 109 [8,5,3] => 109 [8,5,2,1] => 108 [8,5,1,1,1] => 106 [8,4,4] => 108 [8,4,3,1] => 107 [8,4,2,2] => 106 [8,4,2,1,1] => 105 [8,4,1,1,1,1] => 102 [8,3,3,2] => 105 [8,3,3,1,1] => 104 [8,3,2,2,1] => 103 [8,3,2,1,1,1] => 101 [8,3,1,1,1,1,1] => 97 [8,2,2,2,2] => 100 [8,2,2,2,1,1] => 99 [8,2,2,1,1,1,1] => 96 [8,2,1,1,1,1,1,1] => 91 [8,1,1,1,1,1,1,1,1] => 84 [7,7,2] => 109 [7,7,1,1] => 108 [7,6,3] => 108 [7,6,2,1] => 107 [7,6,1,1,1] => 105 [7,5,4] => 107 [7,5,3,1] => 106 [7,5,2,2] => 105 [7,5,2,1,1] => 104 [7,5,1,1,1,1] => 101 [7,4,4,1] => 105 [7,4,3,2] => 104 [7,4,3,1,1] => 103 [7,4,2,2,1] => 102 [7,4,2,1,1,1] => 100 [7,4,1,1,1,1,1] => 96 [7,3,3,3] => 102 [7,3,3,2,1] => 101 [7,3,3,1,1,1] => 99 [7,3,2,2,2] => 99 [7,3,2,2,1,1] => 98 [7,3,2,1,1,1,1] => 95 [7,3,1,1,1,1,1,1] => 90 [7,2,2,2,2,1] => 95 [7,2,2,2,1,1,1] => 93 [7,2,2,1,1,1,1,1] => 89 [7,2,1,1,1,1,1,1,1] => 83 [7,1,1,1,1,1,1,1,1,1] => 75 [6,6,4] => 106 [6,6,3,1] => 105 [6,6,2,2] => 104 [6,6,2,1,1] => 103 [6,6,1,1,1,1] => 100 [6,5,5] => 105 [6,5,4,1] => 104 [6,5,3,2] => 103 [6,5,3,1,1] => 102 [6,5,2,2,1] => 101 [6,5,2,1,1,1] => 99 [6,5,1,1,1,1,1] => 95 [6,4,4,2] => 102 [6,4,4,1,1] => 101 [6,4,3,3] => 101 [6,4,3,2,1] => 100 [6,4,3,1,1,1] => 98 [6,4,2,2,2] => 98 [6,4,2,2,1,1] => 97 [6,4,2,1,1,1,1] => 94 [6,4,1,1,1,1,1,1] => 89 [6,3,3,3,1] => 98 [6,3,3,2,2] => 97 [6,3,3,2,1,1] => 96 [6,3,3,1,1,1,1] => 93 [6,3,2,2,2,1] => 94 [6,3,2,2,1,1,1] => 92 [6,3,2,1,1,1,1,1] => 88 [6,3,1,1,1,1,1,1,1] => 82 [6,2,2,2,2,2] => 90 [6,2,2,2,2,1,1] => 89 [6,2,2,2,1,1,1,1] => 86 [6,2,2,1,1,1,1,1,1] => 81 [6,2,1,1,1,1,1,1,1,1] => 74 [6,1,1,1,1,1,1,1,1,1,1] => 65 [5,5,5,1] => 102 [5,5,4,2] => 101 [5,5,4,1,1] => 100 [5,5,3,3] => 100 [5,5,3,2,1] => 99 [5,5,3,1,1,1] => 97 [5,5,2,2,2] => 97 [5,5,2,2,1,1] => 96 [5,5,2,1,1,1,1] => 93 [5,5,1,1,1,1,1,1] => 88 [5,4,4,3] => 99 [5,4,4,2,1] => 98 [5,4,4,1,1,1] => 96 [5,4,3,3,1] => 97 [5,4,3,2,2] => 96 [5,4,3,2,1,1] => 95 [5,4,3,1,1,1,1] => 92 [5,4,2,2,2,1] => 93 [5,4,2,2,1,1,1] => 91 [5,4,2,1,1,1,1,1] => 87 [5,4,1,1,1,1,1,1,1] => 81 [5,3,3,3,2] => 94 [5,3,3,3,1,1] => 93 [5,3,3,2,2,1] => 92 [5,3,3,2,1,1,1] => 90 [5,3,3,1,1,1,1,1] => 86 [5,3,2,2,2,2] => 89 [5,3,2,2,2,1,1] => 88 [5,3,2,2,1,1,1,1] => 85 [5,3,2,1,1,1,1,1,1] => 80 [5,3,1,1,1,1,1,1,1,1] => 73 [5,2,2,2,2,2,1] => 84 [5,2,2,2,2,1,1,1] => 82 [5,2,2,2,1,1,1,1,1] => 78 [5,2,2,1,1,1,1,1,1,1] => 72 [5,2,1,1,1,1,1,1,1,1,1] => 64 [5,1,1,1,1,1,1,1,1,1,1,1] => 54 [4,4,4,4] => 96 [4,4,4,3,1] => 95 [4,4,4,2,2] => 94 [4,4,4,2,1,1] => 93 [4,4,4,1,1,1,1] => 90 [4,4,3,3,2] => 93 [4,4,3,3,1,1] => 92 [4,4,3,2,2,1] => 91 [4,4,3,2,1,1,1] => 89 [4,4,3,1,1,1,1,1] => 85 [4,4,2,2,2,2] => 88 [4,4,2,2,2,1,1] => 87 [4,4,2,2,1,1,1,1] => 84 [4,4,2,1,1,1,1,1,1] => 79 [4,4,1,1,1,1,1,1,1,1] => 72 [4,3,3,3,3] => 90 [4,3,3,3,2,1] => 89 [4,3,3,3,1,1,1] => 87 [4,3,3,2,2,2] => 87 [4,3,3,2,2,1,1] => 86 [4,3,3,2,1,1,1,1] => 83 [4,3,3,1,1,1,1,1,1] => 78 [4,3,2,2,2,2,1] => 83 [4,3,2,2,2,1,1,1] => 81 [4,3,2,2,1,1,1,1,1] => 77 [4,3,2,1,1,1,1,1,1,1] => 71 [4,3,1,1,1,1,1,1,1,1,1] => 63 [4,2,2,2,2,2,2] => 78 [4,2,2,2,2,2,1,1] => 77 [4,2,2,2,2,1,1,1,1] => 74 [4,2,2,2,1,1,1,1,1,1] => 69 [4,2,2,1,1,1,1,1,1,1,1] => 62 [4,2,1,1,1,1,1,1,1,1,1,1] => 53 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 42 [3,3,3,3,3,1] => 85 [3,3,3,3,2,2] => 84 [3,3,3,3,2,1,1] => 83 [3,3,3,3,1,1,1,1] => 80 [3,3,3,2,2,2,1] => 81 [3,3,3,2,2,1,1,1] => 79 [3,3,3,2,1,1,1,1,1] => 75 [3,3,3,1,1,1,1,1,1,1] => 69 [3,3,2,2,2,2,2] => 77 [3,3,2,2,2,2,1,1] => 76 [3,3,2,2,2,1,1,1,1] => 73 [3,3,2,2,1,1,1,1,1,1] => 68 [3,3,2,1,1,1,1,1,1,1,1] => 61 [3,3,1,1,1,1,1,1,1,1,1,1] => 52 [3,2,2,2,2,2,2,1] => 71 [3,2,2,2,2,2,1,1,1] => 69 [3,2,2,2,2,1,1,1,1,1] => 65 [3,2,2,2,1,1,1,1,1,1,1] => 59 [3,2,2,1,1,1,1,1,1,1,1,1] => 51 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 41 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 29 [2,2,2,2,2,2,2,2] => 64 [2,2,2,2,2,2,2,1,1] => 63 [2,2,2,2,2,2,1,1,1,1] => 60 [2,2,2,2,2,1,1,1,1,1,1] => 55 [2,2,2,2,1,1,1,1,1,1,1,1] => 48 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 39 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 28 [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 15 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [17] => 136 [16,1] => 135 [15,2] => 134 [15,1,1] => 133 [14,3] => 133 [14,2,1] => 132 [14,1,1,1] => 130 [13,4] => 132 [13,3,1] => 131 [13,2,2] => 130 [13,2,1,1] => 129 [13,1,1,1,1] => 126 [12,5] => 131 [12,4,1] => 130 [12,3,2] => 129 [12,3,1,1] => 128 [12,2,2,1] => 127 [12,2,1,1,1] => 125 [12,1,1,1,1,1] => 121 [11,6] => 130 [11,5,1] => 129 [11,4,2] => 128 [11,4,1,1] => 127 [11,3,3] => 127 [11,3,2,1] => 126 [11,3,1,1,1] => 124 [11,2,2,2] => 124 [11,2,2,1,1] => 123 [11,2,1,1,1,1] => 120 [11,1,1,1,1,1,1] => 115 [10,7] => 129 [10,6,1] => 128 [10,5,2] => 127 [10,5,1,1] => 126 [10,4,3] => 126 [10,4,2,1] => 125 [10,4,1,1,1] => 123 [10,3,3,1] => 124 [10,3,2,2] => 123 [10,3,2,1,1] => 122 [10,3,1,1,1,1] => 119 [10,2,2,2,1] => 120 [10,2,2,1,1,1] => 118 [10,2,1,1,1,1,1] => 114 [10,1,1,1,1,1,1,1] => 108 [9,8] => 128 [9,7,1] => 127 [9,6,2] => 126 [9,6,1,1] => 125 [9,5,3] => 125 [9,5,2,1] => 124 [9,5,1,1,1] => 122 [9,4,4] => 124 [9,4,3,1] => 123 [9,4,2,2] => 122 [9,4,2,1,1] => 121 [9,4,1,1,1,1] => 118 [9,3,3,2] => 121 [9,3,3,1,1] => 120 [9,3,2,2,1] => 119 [9,3,2,1,1,1] => 117 [9,3,1,1,1,1,1] => 113 [9,2,2,2,2] => 116 [9,2,2,2,1,1] => 115 [9,2,2,1,1,1,1] => 112 [9,2,1,1,1,1,1,1] => 107 [9,1,1,1,1,1,1,1,1] => 100 [8,8,1] => 126 [8,7,2] => 125 [8,7,1,1] => 124 [8,6,3] => 124 [8,6,2,1] => 123 [8,6,1,1,1] => 121 [8,5,4] => 123 [8,5,3,1] => 122 [8,5,2,2] => 121 [8,5,2,1,1] => 120 [8,5,1,1,1,1] => 117 [8,4,4,1] => 121 [8,4,3,2] => 120 [8,4,3,1,1] => 119 [8,4,2,2,1] => 118 [8,4,2,1,1,1] => 116 [8,4,1,1,1,1,1] => 112 [8,3,3,3] => 118 [8,3,3,2,1] => 117 [8,3,3,1,1,1] => 115 [8,3,2,2,2] => 115 [8,3,2,2,1,1] => 114 [8,3,2,1,1,1,1] => 111 [8,3,1,1,1,1,1,1] => 106 [8,2,2,2,2,1] => 111 [8,2,2,2,1,1,1] => 109 [8,2,2,1,1,1,1,1] => 105 [8,2,1,1,1,1,1,1,1] => 99 [8,1,1,1,1,1,1,1,1,1] => 91 [7,7,3] => 123 [7,7,2,1] => 122 [7,7,1,1,1] => 120 [7,6,4] => 122 [7,6,3,1] => 121 [7,6,2,2] => 120 [7,6,2,1,1] => 119 [7,6,1,1,1,1] => 116 [7,5,5] => 121 [7,5,4,1] => 120 [7,5,3,2] => 119 [7,5,3,1,1] => 118 [7,5,2,2,1] => 117 [7,5,2,1,1,1] => 115 [7,5,1,1,1,1,1] => 111 [7,4,4,2] => 118 [7,4,4,1,1] => 117 [7,4,3,3] => 117 [7,4,3,2,1] => 116 [7,4,3,1,1,1] => 114 [7,4,2,2,2] => 114 [7,4,2,2,1,1] => 113 [7,4,2,1,1,1,1] => 110 [7,4,1,1,1,1,1,1] => 105 [7,3,3,3,1] => 114 [7,3,3,2,2] => 113 [7,3,3,2,1,1] => 112 [7,3,3,1,1,1,1] => 109 [7,3,2,2,2,1] => 110 [7,3,2,2,1,1,1] => 108 [7,3,2,1,1,1,1,1] => 104 [7,3,1,1,1,1,1,1,1] => 98 [7,2,2,2,2,2] => 106 [7,2,2,2,2,1,1] => 105 [7,2,2,2,1,1,1,1] => 102 [7,2,2,1,1,1,1,1,1] => 97 [7,2,1,1,1,1,1,1,1,1] => 90 [7,1,1,1,1,1,1,1,1,1,1] => 81 [6,6,5] => 120 [6,6,4,1] => 119 [6,6,3,2] => 118 [6,6,3,1,1] => 117 [6,6,2,2,1] => 116 [6,6,2,1,1,1] => 114 [6,6,1,1,1,1,1] => 110 [6,5,5,1] => 118 [6,5,4,2] => 117 [6,5,4,1,1] => 116 [6,5,3,3] => 116 [6,5,3,2,1] => 115 [6,5,3,1,1,1] => 113 [6,5,2,2,2] => 113 [6,5,2,2,1,1] => 112 [6,5,2,1,1,1,1] => 109 [6,5,1,1,1,1,1,1] => 104 [6,4,4,3] => 115 [6,4,4,2,1] => 114 [6,4,4,1,1,1] => 112 [6,4,3,3,1] => 113 [6,4,3,2,2] => 112 [6,4,3,2,1,1] => 111 [6,4,3,1,1,1,1] => 108 [6,4,2,2,2,1] => 109 [6,4,2,2,1,1,1] => 107 [6,4,2,1,1,1,1,1] => 103 [6,4,1,1,1,1,1,1,1] => 97 [6,3,3,3,2] => 110 [6,3,3,3,1,1] => 109 [6,3,3,2,2,1] => 108 [6,3,3,2,1,1,1] => 106 [6,3,3,1,1,1,1,1] => 102 [6,3,2,2,2,2] => 105 [6,3,2,2,2,1,1] => 104 [6,3,2,2,1,1,1,1] => 101 [6,3,2,1,1,1,1,1,1] => 96 [6,3,1,1,1,1,1,1,1,1] => 89 [6,2,2,2,2,2,1] => 100 [6,2,2,2,2,1,1,1] => 98 [6,2,2,2,1,1,1,1,1] => 94 [6,2,2,1,1,1,1,1,1,1] => 88 [6,2,1,1,1,1,1,1,1,1,1] => 80 [6,1,1,1,1,1,1,1,1,1,1,1] => 70 [5,5,5,2] => 115 [5,5,5,1,1] => 114 [5,5,4,3] => 114 [5,5,4,2,1] => 113 [5,5,4,1,1,1] => 111 [5,5,3,3,1] => 112 [5,5,3,2,2] => 111 [5,5,3,2,1,1] => 110 [5,5,3,1,1,1,1] => 107 [5,5,2,2,2,1] => 108 [5,5,2,2,1,1,1] => 106 [5,5,2,1,1,1,1,1] => 102 [5,5,1,1,1,1,1,1,1] => 96 [5,4,4,4] => 112 [5,4,4,3,1] => 111 [5,4,4,2,2] => 110 [5,4,4,2,1,1] => 109 [5,4,4,1,1,1,1] => 106 [5,4,3,3,2] => 109 [5,4,3,3,1,1] => 108 [5,4,3,2,2,1] => 107 [5,4,3,2,1,1,1] => 105 [5,4,3,1,1,1,1,1] => 101 [5,4,2,2,2,2] => 104 [5,4,2,2,2,1,1] => 103 [5,4,2,2,1,1,1,1] => 100 [5,4,2,1,1,1,1,1,1] => 95 [5,4,1,1,1,1,1,1,1,1] => 88 [5,3,3,3,3] => 106 [5,3,3,3,2,1] => 105 [5,3,3,3,1,1,1] => 103 [5,3,3,2,2,2] => 103 [5,3,3,2,2,1,1] => 102 [5,3,3,2,1,1,1,1] => 99 [5,3,3,1,1,1,1,1,1] => 94 [5,3,2,2,2,2,1] => 99 [5,3,2,2,2,1,1,1] => 97 [5,3,2,2,1,1,1,1,1] => 93 [5,3,2,1,1,1,1,1,1,1] => 87 [5,3,1,1,1,1,1,1,1,1,1] => 79 [5,2,2,2,2,2,2] => 94 [5,2,2,2,2,2,1,1] => 93 [5,2,2,2,2,1,1,1,1] => 90 [5,2,2,2,1,1,1,1,1,1] => 85 [5,2,2,1,1,1,1,1,1,1,1] => 78 [5,2,1,1,1,1,1,1,1,1,1,1] => 69 [5,1,1,1,1,1,1,1,1,1,1,1,1] => 58 [4,4,4,4,1] => 108 [4,4,4,3,2] => 107 [4,4,4,3,1,1] => 106 [4,4,4,2,2,1] => 105 [4,4,4,2,1,1,1] => 103 [4,4,4,1,1,1,1,1] => 99 [4,4,3,3,3] => 105 [4,4,3,3,2,1] => 104 [4,4,3,3,1,1,1] => 102 [4,4,3,2,2,2] => 102 [4,4,3,2,2,1,1] => 101 [4,4,3,2,1,1,1,1] => 98 [4,4,3,1,1,1,1,1,1] => 93 [4,4,2,2,2,2,1] => 98 [4,4,2,2,2,1,1,1] => 96 [4,4,2,2,1,1,1,1,1] => 92 [4,4,2,1,1,1,1,1,1,1] => 86 [4,4,1,1,1,1,1,1,1,1,1] => 78 [4,3,3,3,3,1] => 101 [4,3,3,3,2,2] => 100 [4,3,3,3,2,1,1] => 99 [4,3,3,3,1,1,1,1] => 96 [4,3,3,2,2,2,1] => 97 [4,3,3,2,2,1,1,1] => 95 [4,3,3,2,1,1,1,1,1] => 91 [4,3,3,1,1,1,1,1,1,1] => 85 [4,3,2,2,2,2,2] => 93 [4,3,2,2,2,2,1,1] => 92 [4,3,2,2,2,1,1,1,1] => 89 [4,3,2,2,1,1,1,1,1,1] => 84 [4,3,2,1,1,1,1,1,1,1,1] => 77 [4,3,1,1,1,1,1,1,1,1,1,1] => 68 [4,2,2,2,2,2,2,1] => 87 [4,2,2,2,2,2,1,1,1] => 85 [4,2,2,2,2,1,1,1,1,1] => 81 [4,2,2,2,1,1,1,1,1,1,1] => 75 [4,2,2,1,1,1,1,1,1,1,1,1] => 67 [4,2,1,1,1,1,1,1,1,1,1,1,1] => 57 [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 45 [3,3,3,3,3,2] => 96 [3,3,3,3,3,1,1] => 95 [3,3,3,3,2,2,1] => 94 [3,3,3,3,2,1,1,1] => 92 [3,3,3,3,1,1,1,1,1] => 88 [3,3,3,2,2,2,2] => 91 [3,3,3,2,2,2,1,1] => 90 [3,3,3,2,2,1,1,1,1] => 87 [3,3,3,2,1,1,1,1,1,1] => 82 [3,3,3,1,1,1,1,1,1,1,1] => 75 [3,3,2,2,2,2,2,1] => 86 [3,3,2,2,2,2,1,1,1] => 84 [3,3,2,2,2,1,1,1,1,1] => 80 [3,3,2,2,1,1,1,1,1,1,1] => 74 [3,3,2,1,1,1,1,1,1,1,1,1] => 66 [3,3,1,1,1,1,1,1,1,1,1,1,1] => 56 [3,2,2,2,2,2,2,2] => 80 [3,2,2,2,2,2,2,1,1] => 79 [3,2,2,2,2,2,1,1,1,1] => 76 [3,2,2,2,2,1,1,1,1,1,1] => 71 [3,2,2,2,1,1,1,1,1,1,1,1] => 64 [3,2,2,1,1,1,1,1,1,1,1,1,1] => 55 ----------------------------------------------------------------------------- Created: May 12, 2020 at 15:22 by Christian Stump ----------------------------------------------------------------------------- Last Updated: May 12, 2020 at 15:22 by Christian Stump