***************************************************************************** * 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: St001360 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of covering relations in Young's lattice below a partition. ----------------------------------------------------------------------------- References: [1] Hopkins, S. Formula for number of edges in Hasse diagram of Young's lattice interval [[MathOverflow:324546]] ----------------------------------------------------------------------------- Code: @cached_function def YoungsLattice(n): return posets.YoungsLattice(n) def statistic(la): Y = YoungsLattice(la.size()) return len(Y.subposet(Y.principal_order_ideal(la)).cover_relations()) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 2 [1,1] => 2 [3] => 3 [2,1] => 5 [1,1,1] => 3 [4] => 4 [3,1] => 8 [2,2] => 6 [2,1,1] => 8 [1,1,1,1] => 4 [5] => 5 [4,1] => 11 [3,2] => 11 [3,1,1] => 13 [2,2,1] => 11 [2,1,1,1] => 11 [1,1,1,1,1] => 5 [6] => 6 [5,1] => 14 [4,2] => 16 [4,1,1] => 18 [3,3] => 12 [3,2,1] => 21 [3,1,1,1] => 18 [2,2,2] => 12 [2,2,1,1] => 16 [2,1,1,1,1] => 14 [1,1,1,1,1,1] => 6 [7] => 7 [6,1] => 17 [5,2] => 21 [5,1,1] => 23 [4,3] => 19 [4,2,1] => 31 [4,1,1,1] => 25 [3,3,1] => 24 [3,2,2] => 24 [3,2,1,1] => 31 [3,1,1,1,1] => 23 [2,2,2,1] => 19 [2,2,1,1,1] => 21 [2,1,1,1,1,1] => 17 [1,1,1,1,1,1,1] => 7 [8] => 8 [7,1] => 20 [6,2] => 26 [6,1,1] => 28 [5,3] => 26 [5,2,1] => 41 [5,1,1,1] => 32 [4,4] => 20 [4,3,1] => 39 [4,2,2] => 36 [4,2,1,1] => 46 [4,1,1,1,1] => 32 [3,3,2] => 29 [3,3,1,1] => 36 [3,2,2,1] => 39 [3,2,1,1,1] => 41 [3,1,1,1,1,1] => 28 [2,2,2,2] => 20 [2,2,2,1,1] => 26 [2,2,1,1,1,1] => 26 [2,1,1,1,1,1,1] => 20 [1,1,1,1,1,1,1,1] => 8 [9] => 9 [8,1] => 23 [7,2] => 31 [7,1,1] => 33 [6,3] => 33 [6,2,1] => 51 [6,1,1,1] => 39 [5,4] => 29 [5,3,1] => 54 [5,2,2] => 48 [5,2,1,1] => 61 [5,1,1,1,1] => 41 [4,4,1] => 42 [4,3,2] => 49 [4,3,1,1] => 59 [4,2,2,1] => 59 [4,2,1,1,1] => 61 [4,1,1,1,1,1] => 39 [3,3,3] => 30 [3,3,2,1] => 49 [3,3,1,1,1] => 48 [3,2,2,2] => 42 [3,2,2,1,1] => 54 [3,2,1,1,1,1] => 51 [3,1,1,1,1,1,1] => 33 [2,2,2,2,1] => 29 [2,2,2,1,1,1] => 33 [2,2,1,1,1,1,1] => 31 [2,1,1,1,1,1,1,1] => 23 [1,1,1,1,1,1,1,1,1] => 9 [10] => 10 [9,1] => 26 [8,2] => 36 [8,1,1] => 38 [7,3] => 40 [7,2,1] => 61 [7,1,1,1] => 46 [6,4] => 38 [6,3,1] => 69 [6,2,2] => 60 [6,2,1,1] => 76 [6,1,1,1,1] => 50 [5,5] => 30 [5,4,1] => 62 [5,3,2] => 69 [5,3,1,1] => 82 [5,2,2,1] => 79 [5,2,1,1,1] => 81 [5,1,1,1,1,1] => 50 [4,4,2] => 54 [4,4,1,1] => 64 [4,3,3] => 52 [4,3,2,1] => 84 [4,3,1,1,1] => 79 [4,2,2,2] => 64 [4,2,2,1,1] => 82 [4,2,1,1,1,1] => 76 [4,1,1,1,1,1,1] => 46 [3,3,3,1] => 52 [3,3,2,2] => 54 [3,3,2,1,1] => 69 [3,3,1,1,1,1] => 60 [3,2,2,2,1] => 62 [3,2,2,1,1,1] => 69 [3,2,1,1,1,1,1] => 61 [3,1,1,1,1,1,1,1] => 38 [2,2,2,2,2] => 30 [2,2,2,2,1,1] => 38 [2,2,2,1,1,1,1] => 40 [2,2,1,1,1,1,1,1] => 36 [2,1,1,1,1,1,1,1,1] => 26 [1,1,1,1,1,1,1,1,1,1] => 10 [11] => 11 [10,1] => 29 [9,2] => 41 [9,1,1] => 43 [8,3] => 47 [8,2,1] => 71 [8,1,1,1] => 53 [7,4] => 47 [7,3,1] => 84 [7,2,2] => 72 [7,2,1,1] => 91 [7,1,1,1,1] => 59 [6,5] => 41 [6,4,1] => 82 [6,3,2] => 89 [6,3,1,1] => 105 [6,2,2,1] => 99 [6,2,1,1,1] => 101 [6,1,1,1,1,1] => 61 [5,5,1] => 65 [5,4,2] => 82 [5,4,1,1] => 95 [5,3,3] => 74 [5,3,2,1] => 119 [5,3,1,1,1] => 110 [5,2,2,2] => 86 [5,2,2,1,1] => 110 [5,2,1,1,1,1] => 101 [5,1,1,1,1,1,1] => 59 [4,4,3] => 59 [4,4,2,1] => 94 [4,4,1,1,1] => 86 [4,3,3,1] => 92 [4,3,2,2] => 94 [4,3,2,1,1] => 119 [4,3,1,1,1,1] => 99 [4,2,2,2,1] => 95 [4,2,2,1,1,1] => 105 [4,2,1,1,1,1,1] => 91 [4,1,1,1,1,1,1,1] => 53 [3,3,3,2] => 59 [3,3,3,1,1] => 74 [3,3,2,2,1] => 82 [3,3,2,1,1,1] => 89 [3,3,1,1,1,1,1] => 72 [3,2,2,2,2] => 65 [3,2,2,2,1,1] => 82 [3,2,2,1,1,1,1] => 84 [3,2,1,1,1,1,1,1] => 71 [3,1,1,1,1,1,1,1,1] => 43 [2,2,2,2,2,1] => 41 [2,2,2,2,1,1,1] => 47 [2,2,2,1,1,1,1,1] => 47 [2,2,1,1,1,1,1,1,1] => 41 [2,1,1,1,1,1,1,1,1,1] => 29 [1,1,1,1,1,1,1,1,1,1,1] => 11 [12] => 12 [11,1] => 32 [10,2] => 46 [10,1,1] => 48 [9,3] => 54 [9,2,1] => 81 [9,1,1,1] => 60 [8,4] => 56 [8,3,1] => 99 [8,2,2] => 84 [8,2,1,1] => 106 [8,1,1,1,1] => 68 [7,5] => 52 [7,4,1] => 102 [7,3,2] => 109 [7,3,1,1] => 128 [7,2,2,1] => 119 [7,2,1,1,1] => 121 [7,1,1,1,1,1] => 72 [6,6] => 42 [6,5,1] => 90 [6,4,2] => 110 [6,4,1,1] => 126 [6,3,3] => 96 [6,3,2,1] => 154 [6,3,1,1,1] => 141 [6,2,2,2] => 108 [6,2,2,1,1] => 138 [6,2,1,1,1,1] => 126 [6,1,1,1,1,1,1] => 72 [5,5,2] => 87 [5,5,1,1] => 100 [5,4,3] => 92 [5,4,2,1] => 144 [5,4,1,1,1] => 128 [5,3,3,1] => 132 [5,3,2,2] => 134 [5,3,2,1,1] => 169 [5,3,1,1,1,1] => 138 [5,2,2,2,1] => 128 [5,2,2,1,1,1] => 141 [5,2,1,1,1,1,1] => 121 [5,1,1,1,1,1,1,1] => 68 [4,4,4] => 60 [4,4,3,1] => 107 [4,4,2,2] => 106 [4,4,2,1,1] => 134 [4,4,1,1,1,1] => 108 [4,3,3,2] => 107 [4,3,3,1,1] => 132 [4,3,2,2,1] => 144 [4,3,2,1,1,1] => 154 [4,3,1,1,1,1,1] => 119 [4,2,2,2,2] => 100 [4,2,2,2,1,1] => 126 [4,2,2,1,1,1,1] => 128 [4,2,1,1,1,1,1,1] => 106 [4,1,1,1,1,1,1,1,1] => 60 [3,3,3,3] => 60 [3,3,3,2,1] => 92 [3,3,3,1,1,1] => 96 [3,3,2,2,2] => 87 [3,3,2,2,1,1] => 110 [3,3,2,1,1,1,1] => 109 [3,3,1,1,1,1,1,1] => 84 [3,2,2,2,2,1] => 90 [3,2,2,2,1,1,1] => 102 [3,2,2,1,1,1,1,1] => 99 [3,2,1,1,1,1,1,1,1] => 81 [3,1,1,1,1,1,1,1,1,1] => 48 [2,2,2,2,2,2] => 42 [2,2,2,2,2,1,1] => 52 [2,2,2,2,1,1,1,1] => 56 [2,2,2,1,1,1,1,1,1] => 54 [2,2,1,1,1,1,1,1,1,1] => 46 [2,1,1,1,1,1,1,1,1,1,1] => 32 [1,1,1,1,1,1,1,1,1,1,1,1] => 12 [13] => 13 [12,1] => 35 [11,2] => 51 [11,1,1] => 53 [10,3] => 61 [10,2,1] => 91 [10,1,1,1] => 67 [9,4] => 65 [9,3,1] => 114 [9,2,2] => 96 [9,2,1,1] => 121 [9,1,1,1,1] => 77 [8,5] => 63 [8,4,1] => 122 [8,3,2] => 129 [8,3,1,1] => 151 [8,2,2,1] => 139 [8,2,1,1,1] => 141 [8,1,1,1,1,1] => 83 [7,6] => 55 [7,5,1] => 115 [7,4,2] => 138 [7,4,1,1] => 157 [7,3,3] => 118 [7,3,2,1] => 189 [7,3,1,1,1] => 172 [7,2,2,2] => 130 [7,2,2,1,1] => 166 [7,2,1,1,1,1] => 151 [7,1,1,1,1,1,1] => 85 [6,6,1] => 93 [6,5,2] => 123 [6,5,1,1] => 139 [6,4,3] => 125 [6,4,2,1] => 194 [6,4,1,1,1] => 170 [6,3,3,1] => 172 [6,3,2,2] => 174 [6,3,2,1,1] => 219 [6,3,1,1,1,1] => 177 [6,2,2,2,1] => 161 [6,2,2,1,1,1] => 177 [6,2,1,1,1,1,1] => 151 [6,1,1,1,1,1,1,1] => 83 [5,5,3] => 99 [5,5,2,1] => 154 [5,5,1,1,1] => 135 [5,4,4] => 95 [5,4,3,1] => 169 [5,4,2,2] => 164 [5,4,2,1,1] => 206 [5,4,1,1,1,1] => 161 [5,3,3,2] => 155 [5,3,3,1,1] => 190 [5,3,2,2,1] => 206 [5,3,2,1,1,1] => 219 [5,3,1,1,1,1,1] => 166 [5,2,2,2,2] => 135 [5,2,2,2,1,1] => 170 [5,2,2,1,1,1,1] => 172 [5,2,1,1,1,1,1,1] => 141 [5,1,1,1,1,1,1,1,1] => 77 [4,4,4,1] => 110 [4,4,3,2] => 127 [4,4,3,1,1] => 155 [4,4,2,2,1] => 164 [4,4,2,1,1,1] => 174 [4,4,1,1,1,1,1] => 130 [4,3,3,3] => 110 [4,3,3,2,1] => 169 [4,3,3,1,1,1] => 172 [4,3,2,2,2] => 154 [4,3,2,2,1,1] => 194 [4,3,2,1,1,1,1] => 189 [4,3,1,1,1,1,1,1] => 139 [4,2,2,2,2,1] => 139 [4,2,2,2,1,1,1] => 157 [4,2,2,1,1,1,1,1] => 151 [4,2,1,1,1,1,1,1,1] => 121 [4,1,1,1,1,1,1,1,1,1] => 67 [3,3,3,3,1] => 95 [3,3,3,2,2] => 99 [3,3,3,2,1,1] => 125 [3,3,3,1,1,1,1] => 118 [3,3,2,2,2,1] => 123 [3,3,2,2,1,1,1] => 138 [3,3,2,1,1,1,1,1] => 129 [3,3,1,1,1,1,1,1,1] => 96 [3,2,2,2,2,2] => 93 [3,2,2,2,2,1,1] => 115 [3,2,2,2,1,1,1,1] => 122 [3,2,2,1,1,1,1,1,1] => 114 [3,2,1,1,1,1,1,1,1,1] => 91 [3,1,1,1,1,1,1,1,1,1,1] => 53 [2,2,2,2,2,2,1] => 55 [2,2,2,2,2,1,1,1] => 63 [2,2,2,2,1,1,1,1,1] => 65 [2,2,2,1,1,1,1,1,1,1] => 61 [2,2,1,1,1,1,1,1,1,1,1] => 51 [2,1,1,1,1,1,1,1,1,1,1,1] => 35 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 13 [14] => 14 [13,1] => 38 [12,2] => 56 [12,1,1] => 58 [11,3] => 68 [11,2,1] => 101 [11,1,1,1] => 74 [10,4] => 74 [10,3,1] => 129 [10,2,2] => 108 [10,2,1,1] => 136 [10,1,1,1,1] => 86 [9,5] => 74 [9,4,1] => 142 [9,3,2] => 149 [9,3,1,1] => 174 [9,2,2,1] => 159 [9,2,1,1,1] => 161 [9,1,1,1,1,1] => 94 [8,6] => 68 [8,5,1] => 140 [8,4,2] => 166 [8,4,1,1] => 188 [8,3,3] => 140 [8,3,2,1] => 224 [8,3,1,1,1] => 203 [8,2,2,2] => 152 [8,2,2,1,1] => 194 [8,2,1,1,1,1] => 176 [8,1,1,1,1,1,1] => 98 [7,7] => 56 [7,6,1] => 123 [7,5,2] => 159 [7,5,1,1] => 178 [7,4,3] => 158 [7,4,2,1] => 244 [7,4,1,1,1] => 212 [7,3,3,1] => 212 [7,3,2,2] => 214 [7,3,2,1,1] => 269 [7,3,1,1,1,1] => 216 [7,2,2,2,1] => 194 [7,2,2,1,1,1] => 213 [7,2,1,1,1,1,1] => 181 [7,1,1,1,1,1,1,1] => 98 [6,6,2] => 128 [6,6,1,1] => 144 [6,5,3] => 143 [6,5,2,1] => 219 [6,5,1,1,1] => 188 [6,4,4] => 130 [6,4,3,1] => 231 [6,4,2,2] => 222 [6,4,2,1,1] => 278 [6,4,1,1,1,1] => 214 [6,3,3,2] => 203 [6,3,3,1,1] => 248 [6,3,2,2,1] => 268 [6,3,2,1,1,1] => 284 [6,3,1,1,1,1,1] => 213 [6,2,2,2,2] => 170 [6,2,2,2,1,1] => 214 [6,2,2,1,1,1,1] => 216 [6,2,1,1,1,1,1,1] => 176 [6,1,1,1,1,1,1,1,1] => 94 [5,5,4] => 104 [5,5,3,1] => 184 [5,5,2,2] => 176 [5,5,2,1,1] => 221 [5,5,1,1,1,1] => 170 [5,4,4,1] => 177 [5,4,3,2] => 204 [5,4,3,1,1] => 246 [5,4,2,2,1] => 255 [5,4,2,1,1,1] => 268 [5,4,1,1,1,1,1] => 194 [5,3,3,3] => 160 [5,3,3,2,1] => 246 [5,3,3,1,1,1] => 248 [5,3,2,2,2] => 221 [5,3,2,2,1,1] => 278 [5,3,2,1,1,1,1] => 269 [5,3,1,1,1,1,1,1] => 194 [5,2,2,2,2,1] => 188 [5,2,2,2,1,1,1] => 212 [5,2,2,1,1,1,1,1] => 203 [5,2,1,1,1,1,1,1,1] => 161 [5,1,1,1,1,1,1,1,1,1] => 86 [4,4,4,2] => 132 [4,4,4,1,1] => 160 [4,4,3,3] => 132 [4,4,3,2,1] => 204 [4,4,3,1,1,1] => 203 [4,4,2,2,2] => 176 [4,4,2,2,1,1] => 222 [4,4,2,1,1,1,1] => 214 [4,4,1,1,1,1,1,1] => 152 [4,3,3,3,1] => 177 [4,3,3,2,2] => 184 [4,3,3,2,1,1] => 231 [4,3,3,1,1,1,1] => 212 [4,3,2,2,2,1] => 219 [4,3,2,2,1,1,1] => 244 [4,3,2,1,1,1,1,1] => 224 [4,3,1,1,1,1,1,1,1] => 159 [4,2,2,2,2,2] => 144 [4,2,2,2,2,1,1] => 178 [4,2,2,2,1,1,1,1] => 188 [4,2,2,1,1,1,1,1,1] => 174 [4,2,1,1,1,1,1,1,1,1] => 136 [4,1,1,1,1,1,1,1,1,1,1] => 74 [3,3,3,3,2] => 104 [3,3,3,3,1,1] => 130 [3,3,3,2,2,1] => 143 [3,3,3,2,1,1,1] => 158 [3,3,3,1,1,1,1,1] => 140 [3,3,2,2,2,2] => 128 [3,3,2,2,2,1,1] => 159 [3,3,2,2,1,1,1,1] => 166 [3,3,2,1,1,1,1,1,1] => 149 [3,3,1,1,1,1,1,1,1,1] => 108 [3,2,2,2,2,2,1] => 123 [3,2,2,2,2,1,1,1] => 140 [3,2,2,2,1,1,1,1,1] => 142 [3,2,2,1,1,1,1,1,1,1] => 129 [3,2,1,1,1,1,1,1,1,1,1] => 101 [3,1,1,1,1,1,1,1,1,1,1,1] => 58 [2,2,2,2,2,2,2] => 56 [2,2,2,2,2,2,1,1] => 68 [2,2,2,2,2,1,1,1,1] => 74 [2,2,2,2,1,1,1,1,1,1] => 74 [2,2,2,1,1,1,1,1,1,1,1] => 68 [2,2,1,1,1,1,1,1,1,1,1,1] => 56 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 38 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 14 [15] => 15 [14,1] => 41 [13,2] => 61 [13,1,1] => 63 [12,3] => 75 [12,2,1] => 111 [12,1,1,1] => 81 [11,4] => 83 [11,3,1] => 144 [11,2,2] => 120 [11,2,1,1] => 151 [11,1,1,1,1] => 95 [10,5] => 85 [10,4,1] => 162 [10,3,2] => 169 [10,3,1,1] => 197 [10,2,2,1] => 179 [10,2,1,1,1] => 181 [10,1,1,1,1,1] => 105 [9,6] => 81 [9,5,1] => 165 [9,4,2] => 194 [9,4,1,1] => 219 [9,3,3] => 162 [9,3,2,1] => 259 [9,3,1,1,1] => 234 [9,2,2,2] => 174 [9,2,2,1,1] => 222 [9,2,1,1,1,1] => 201 [9,1,1,1,1,1,1] => 111 [8,7] => 71 [8,6,1] => 153 [8,5,2] => 195 [8,5,1,1] => 217 [8,4,3] => 191 [8,4,2,1] => 294 [8,4,1,1,1] => 254 [8,3,3,1] => 252 [8,3,2,2] => 254 [8,3,2,1,1] => 319 [8,3,1,1,1,1] => 255 [8,2,2,2,1] => 227 [8,2,2,1,1,1] => 249 [8,2,1,1,1,1,1] => 211 [8,1,1,1,1,1,1,1] => 113 [7,7,1] => 126 [7,6,2] => 172 [7,6,1,1] => 191 [7,5,3] => 187 [7,5,2,1] => 284 [7,5,1,1,1] => 241 [7,4,4] => 165 [7,4,3,1] => 293 [7,4,2,2] => 280 [7,4,2,1,1] => 350 [7,4,1,1,1,1] => 267 [7,3,3,2] => 251 [7,3,3,1,1] => 306 [7,3,2,2,1] => 330 [7,3,2,1,1,1] => 349 [7,3,1,1,1,1,1] => 260 [7,2,2,2,2] => 205 [7,2,2,2,1,1] => 258 [7,2,2,1,1,1,1] => 260 [7,2,1,1,1,1,1,1] => 211 [7,1,1,1,1,1,1,1,1] => 111 [6,6,3] => 150 [6,6,2,1] => 229 [6,6,1,1,1] => 195 [6,5,4] => 153 [6,5,3,1] => 268 [6,5,2,2] => 252 [6,5,2,1,1] => 315 [6,5,1,1,1,1] => 237 [6,4,4,1] => 244 [6,4,3,2] => 281 [6,4,3,1,1] => 337 [6,4,2,2,1] => 346 [6,4,2,1,1,1] => 362 [6,4,1,1,1,1,1] => 258 [6,3,3,3] => 210 [6,3,3,2,1] => 323 [6,3,3,1,1,1] => 324 [6,3,2,2,2] => 288 [6,3,2,2,1,1] => 362 [6,3,2,1,1,1,1] => 349 [6,3,1,1,1,1,1,1] => 249 [6,2,2,2,2,1] => 237 [6,2,2,2,1,1,1] => 267 [6,2,2,1,1,1,1,1] => 255 [6,2,1,1,1,1,1,1,1] => 201 [6,1,1,1,1,1,1,1,1,1] => 105 [5,5,5] => 105 [5,5,4,1] => 197 [5,5,3,2] => 224 [5,5,3,1,1] => 269 [5,5,2,2,1] => 275 [5,5,2,1,1,1] => 288 [5,5,1,1,1,1,1] => 205 [5,4,4,2] => 217 [5,4,4,1,1] => 259 [5,4,3,3] => 214 [5,4,3,2,1] => 330 [5,4,3,1,1,1] => 323 [5,4,2,2,2] => 275 [5,4,2,2,1,1] => 346 [5,4,2,1,1,1,1] => 330 [5,4,1,1,1,1,1,1] => 227 [5,3,3,3,1] => 259 [5,3,3,2,2] => 269 [5,3,3,2,1,1] => 337 [5,3,3,1,1,1,1] => 306 [5,3,2,2,2,1] => 315 [5,3,2,2,1,1,1] => 350 [5,3,2,1,1,1,1,1] => 319 [5,3,1,1,1,1,1,1,1] => 222 [5,2,2,2,2,2] => 195 [5,2,2,2,2,1,1] => 241 [5,2,2,2,1,1,1,1] => 254 [5,2,2,1,1,1,1,1,1] => 234 [5,2,1,1,1,1,1,1,1,1] => 181 [5,1,1,1,1,1,1,1,1,1,1] => 95 [4,4,4,3] => 139 [4,4,4,2,1] => 214 [4,4,4,1,1,1] => 210 [4,4,3,3,1] => 217 [4,4,3,2,2] => 224 [4,4,3,2,1,1] => 281 [4,4,3,1,1,1,1] => 251 [4,4,2,2,2,1] => 252 [4,4,2,2,1,1,1] => 280 [4,4,2,1,1,1,1,1] => 254 [4,4,1,1,1,1,1,1,1] => 174 [4,3,3,3,2] => 197 [4,3,3,3,1,1] => 244 [4,3,3,2,2,1] => 268 [4,3,3,2,1,1,1] => 293 [4,3,3,1,1,1,1,1] => 252 [4,3,2,2,2,2] => 229 [4,3,2,2,2,1,1] => 284 [4,3,2,2,1,1,1,1] => 294 [4,3,2,1,1,1,1,1,1] => 259 [4,3,1,1,1,1,1,1,1,1] => 179 [4,2,2,2,2,2,1] => 191 [4,2,2,2,2,1,1,1] => 217 [4,2,2,2,1,1,1,1,1] => 219 [4,2,2,1,1,1,1,1,1,1] => 197 [4,2,1,1,1,1,1,1,1,1,1] => 151 [4,1,1,1,1,1,1,1,1,1,1,1] => 81 [3,3,3,3,3] => 105 [3,3,3,3,2,1] => 153 [3,3,3,3,1,1,1] => 165 [3,3,3,2,2,2] => 150 [3,3,3,2,2,1,1] => 187 [3,3,3,2,1,1,1,1] => 191 [3,3,3,1,1,1,1,1,1] => 162 [3,3,2,2,2,2,1] => 172 [3,3,2,2,2,1,1,1] => 195 [3,3,2,2,1,1,1,1,1] => 194 [3,3,2,1,1,1,1,1,1,1] => 169 [3,3,1,1,1,1,1,1,1,1,1] => 120 [3,2,2,2,2,2,2] => 126 [3,2,2,2,2,2,1,1] => 153 [3,2,2,2,2,1,1,1,1] => 165 [3,2,2,2,1,1,1,1,1,1] => 162 [3,2,2,1,1,1,1,1,1,1,1] => 144 [3,2,1,1,1,1,1,1,1,1,1,1] => 111 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 63 [2,2,2,2,2,2,2,1] => 71 [2,2,2,2,2,2,1,1,1] => 81 [2,2,2,2,2,1,1,1,1,1] => 85 [2,2,2,2,1,1,1,1,1,1,1] => 83 [2,2,2,1,1,1,1,1,1,1,1,1] => 75 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 61 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 41 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 15 [16] => 16 [15,1] => 44 [14,2] => 66 [14,1,1] => 68 [13,3] => 82 [13,2,1] => 121 [13,1,1,1] => 88 [12,4] => 92 [12,3,1] => 159 [12,2,2] => 132 [12,2,1,1] => 166 [12,1,1,1,1] => 104 [11,5] => 96 [11,4,1] => 182 [11,3,2] => 189 [11,3,1,1] => 220 [11,2,2,1] => 199 [11,2,1,1,1] => 201 [11,1,1,1,1,1] => 116 [10,6] => 94 [10,5,1] => 190 [10,4,2] => 222 [10,4,1,1] => 250 [10,3,3] => 184 [10,3,2,1] => 294 [10,3,1,1,1] => 265 [10,2,2,2] => 196 [10,2,2,1,1] => 250 [10,2,1,1,1,1] => 226 [10,1,1,1,1,1,1] => 124 [9,7] => 86 [9,6,1] => 183 [9,5,2] => 231 [9,5,1,1] => 256 [9,4,3] => 224 [9,4,2,1] => 344 [9,4,1,1,1] => 296 [9,3,3,1] => 292 [9,3,2,2] => 294 [9,3,2,1,1] => 369 [9,3,1,1,1,1] => 294 [9,2,2,2,1] => 260 [9,2,2,1,1,1] => 285 [9,2,1,1,1,1,1] => 241 [9,1,1,1,1,1,1,1] => 128 [8,8] => 72 [8,7,1] => 161 [8,6,2] => 216 [8,6,1,1] => 238 [8,5,3] => 231 [8,5,2,1] => 349 [8,5,1,1,1] => 294 [8,4,4] => 200 [8,4,3,1] => 355 [8,4,2,2] => 338 [8,4,2,1,1] => 422 [8,4,1,1,1,1] => 320 [8,3,3,2] => 299 [8,3,3,1,1] => 364 [8,3,2,2,1] => 392 [8,3,2,1,1,1] => 414 [8,3,1,1,1,1,1] => 307 [8,2,2,2,2] => 240 [8,2,2,2,1,1] => 302 [8,2,2,1,1,1,1] => 304 [8,2,1,1,1,1,1,1] => 246 [8,1,1,1,1,1,1,1,1] => 128 [7,7,2] => 177 [7,7,1,1] => 196 [7,6,3] => 205 [7,6,2,1] => 309 [7,6,1,1,1] => 259 [7,5,4] => 202 [7,5,3,1] => 352 [7,5,2,2] => 328 [7,5,2,1,1] => 409 [7,5,1,1,1,1] => 304 [7,4,4,1] => 311 [7,4,3,2] => 358 [7,4,3,1,1] => 428 [7,4,2,2,1] => 437 [7,4,2,1,1,1] => 456 [7,4,1,1,1,1,1] => 322 [7,3,3,3] => 260 [7,3,3,2,1] => 400 [7,3,3,1,1,1] => 400 [7,3,2,2,2] => 355 [7,3,2,2,1,1] => 446 [7,3,2,1,1,1,1] => 429 [7,3,1,1,1,1,1,1] => 304 [7,2,2,2,2,1] => 286 [7,2,2,2,1,1,1] => 322 [7,2,2,1,1,1,1,1] => 307 [7,2,1,1,1,1,1,1,1] => 241 [7,1,1,1,1,1,1,1,1,1] => 124 [6,6,4] => 162 [6,6,3,1] => 283 [6,6,2,2] => 264 [6,6,2,1,1] => 330 [6,6,1,1,1,1] => 246 [6,5,5] => 156 [6,5,4,1] => 293 [6,5,3,2] => 330 [6,5,3,1,1] => 393 [6,5,2,2,1] => 395 [6,5,2,1,1,1] => 411 [6,5,1,1,1,1,1] => 286 [6,4,4,2] => 302 [6,4,4,1,1] => 358 [6,4,3,3] => 296 [6,4,3,2,1] => 456 [6,4,3,1,1,1] => 443 [6,4,2,2,2] => 374 [6,4,2,2,1,1] => 470 [6,4,2,1,1,1,1] => 446 [6,4,1,1,1,1,1,1] => 302 [6,3,3,3,1] => 341 [6,3,3,2,2] => 354 [6,3,3,2,1,1] => 443 [6,3,3,1,1,1,1] => 400 [6,3,2,2,2,1] => 411 [6,3,2,2,1,1,1] => 456 [6,3,2,1,1,1,1,1] => 414 [6,3,1,1,1,1,1,1,1] => 285 [6,2,2,2,2,2] => 246 [6,2,2,2,2,1,1] => 304 [6,2,2,2,1,1,1,1] => 320 [6,2,2,1,1,1,1,1,1] => 294 [6,2,1,1,1,1,1,1,1,1] => 226 [6,1,1,1,1,1,1,1,1,1,1] => 116 [5,5,5,1] => 200 [5,5,4,2] => 245 [5,5,4,1,1] => 290 [5,5,3,3] => 236 [5,5,3,2,1] => 365 [5,5,3,1,1,1] => 354 [5,5,2,2,2] => 297 [5,5,2,2,1,1] => 374 [5,5,2,1,1,1,1] => 355 [5,5,1,1,1,1,1,1] => 240 [5,4,4,3] => 232 [5,4,4,2,1] => 355 [5,4,4,1,1,1] => 341 [5,4,3,3,1] => 355 [5,4,3,2,2] => 365 [5,4,3,2,1,1] => 456 [5,4,3,1,1,1,1] => 400 [5,4,2,2,2,1] => 395 [5,4,2,2,1,1,1] => 437 [5,4,2,1,1,1,1,1] => 392 [5,4,1,1,1,1,1,1,1] => 260 [5,3,3,3,2] => 290 [5,3,3,3,1,1] => 358 [5,3,3,2,2,1] => 393 [5,3,3,2,1,1,1] => 428 [5,3,3,1,1,1,1,1] => 364 [5,3,2,2,2,2] => 330 [5,3,2,2,2,1,1] => 409 [5,3,2,2,1,1,1,1] => 422 [5,3,2,1,1,1,1,1,1] => 369 [5,3,1,1,1,1,1,1,1,1] => 250 [5,2,2,2,2,2,1] => 259 [5,2,2,2,2,1,1,1] => 294 [5,2,2,2,1,1,1,1,1] => 296 [5,2,2,1,1,1,1,1,1,1] => 265 [5,2,1,1,1,1,1,1,1,1,1] => 201 [5,1,1,1,1,1,1,1,1,1,1,1] => 104 [4,4,4,4] => 140 [4,4,4,3,1] => 232 [4,4,4,2,2] => 236 [4,4,4,2,1,1] => 296 [4,4,4,1,1,1,1] => 260 [4,4,3,3,2] => 245 [4,4,3,3,1,1] => 302 [4,4,3,2,2,1] => 330 [4,4,3,2,1,1,1] => 358 [4,4,3,1,1,1,1,1] => 299 [4,4,2,2,2,2] => 264 [4,4,2,2,2,1,1] => 328 [4,4,2,2,1,1,1,1] => 338 [4,4,2,1,1,1,1,1,1] => 294 [4,4,1,1,1,1,1,1,1,1] => 196 [4,3,3,3,3] => 200 [4,3,3,3,2,1] => 293 [4,3,3,3,1,1,1] => 311 [4,3,3,2,2,2] => 283 [4,3,3,2,2,1,1] => 352 [4,3,3,2,1,1,1,1] => 355 [4,3,3,1,1,1,1,1,1] => 292 [4,3,2,2,2,2,1] => 309 [4,3,2,2,2,1,1,1] => 349 [4,3,2,2,1,1,1,1,1] => 344 [4,3,2,1,1,1,1,1,1,1] => 294 [4,3,1,1,1,1,1,1,1,1,1] => 199 [4,2,2,2,2,2,2] => 196 [4,2,2,2,2,2,1,1] => 238 [4,2,2,2,2,1,1,1,1] => 256 [4,2,2,2,1,1,1,1,1,1] => 250 [4,2,2,1,1,1,1,1,1,1,1] => 220 [4,2,1,1,1,1,1,1,1,1,1,1] => 166 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 88 [3,3,3,3,3,1] => 156 [3,3,3,3,2,2] => 162 [3,3,3,3,2,1,1] => 202 [3,3,3,3,1,1,1,1] => 200 [3,3,3,2,2,2,1] => 205 [3,3,3,2,2,1,1,1] => 231 [3,3,3,2,1,1,1,1,1] => 224 [3,3,3,1,1,1,1,1,1,1] => 184 [3,3,2,2,2,2,2] => 177 [3,3,2,2,2,2,1,1] => 216 [3,3,2,2,2,1,1,1,1] => 231 [3,3,2,2,1,1,1,1,1,1] => 222 [3,3,2,1,1,1,1,1,1,1,1] => 189 [3,3,1,1,1,1,1,1,1,1,1,1] => 132 [3,2,2,2,2,2,2,1] => 161 [3,2,2,2,2,2,1,1,1] => 183 [3,2,2,2,2,1,1,1,1,1] => 190 [3,2,2,2,1,1,1,1,1,1,1] => 182 [3,2,2,1,1,1,1,1,1,1,1,1] => 159 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 121 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 68 [2,2,2,2,2,2,2,2] => 72 [2,2,2,2,2,2,2,1,1] => 86 [2,2,2,2,2,2,1,1,1,1] => 94 [2,2,2,2,2,1,1,1,1,1,1] => 96 [2,2,2,2,1,1,1,1,1,1,1,1] => 92 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 82 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 66 [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 44 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 16 [17] => 17 [16,1] => 47 [15,2] => 71 [15,1,1] => 73 [14,3] => 89 [14,2,1] => 131 [14,1,1,1] => 95 [13,4] => 101 [13,3,1] => 174 [13,2,2] => 144 [13,2,1,1] => 181 [13,1,1,1,1] => 113 [12,5] => 107 [12,4,1] => 202 [12,3,2] => 209 [12,3,1,1] => 243 [12,2,2,1] => 219 [12,2,1,1,1] => 221 [12,1,1,1,1,1] => 127 [11,6] => 107 [11,5,1] => 215 [11,4,2] => 250 [11,4,1,1] => 281 [11,3,3] => 206 [11,3,2,1] => 329 [11,3,1,1,1] => 296 [11,2,2,2] => 218 [11,2,2,1,1] => 278 [11,2,1,1,1,1] => 251 [11,1,1,1,1,1,1] => 137 [10,7] => 101 [10,6,1] => 213 [10,5,2] => 267 [10,5,1,1] => 295 [10,4,3] => 257 [10,4,2,1] => 394 [10,4,1,1,1] => 338 [10,3,3,1] => 332 [10,3,2,2] => 334 [10,3,2,1,1] => 419 [10,3,1,1,1,1] => 333 [10,2,2,2,1] => 293 [10,2,2,1,1,1] => 321 [10,2,1,1,1,1,1] => 271 [10,1,1,1,1,1,1,1] => 143 [9,8] => 89 [9,7,1] => 196 [9,6,2] => 260 [9,6,1,1] => 285 [9,5,3] => 275 [9,5,2,1] => 414 [9,5,1,1,1] => 347 [9,4,4] => 235 [9,4,3,1] => 417 [9,4,2,2] => 396 [9,4,2,1,1] => 494 [9,4,1,1,1,1] => 373 [9,3,3,2] => 347 [9,3,3,1,1] => 422 [9,3,2,2,1] => 454 [9,3,2,1,1,1] => 479 [9,3,1,1,1,1,1] => 354 [9,2,2,2,2] => 275 [9,2,2,2,1,1] => 346 [9,2,2,1,1,1,1] => 348 [9,2,1,1,1,1,1,1] => 281 [9,1,1,1,1,1,1,1,1] => 145 [8,8,1] => 164 [8,7,2] => 229 [8,7,1,1] => 251 [8,6,3] => 260 [8,6,2,1] => 389 [8,6,1,1,1] => 323 [8,5,4] => 251 [8,5,3,1] => 436 [8,5,2,2] => 404 [8,5,2,1,1] => 503 [8,5,1,1,1,1] => 371 [8,4,4,1] => 378 [8,4,3,2] => 435 [8,4,3,1,1] => 519 [8,4,2,2,1] => 528 [8,4,2,1,1,1] => 550 [8,4,1,1,1,1,1] => 386 [8,3,3,3] => 310 [8,3,3,2,1] => 477 [8,3,3,1,1,1] => 476 [8,3,2,2,2] => 422 [8,3,2,2,1,1] => 530 [8,3,2,1,1,1,1] => 509 [8,3,1,1,1,1,1,1] => 359 [8,2,2,2,2,1] => 335 [8,2,2,2,1,1,1] => 377 [8,2,2,1,1,1,1,1] => 359 [8,2,1,1,1,1,1,1,1] => 281 [8,1,1,1,1,1,1,1,1,1] => 143 [7,7,3] => 212 [7,7,2,1] => 319 [7,7,1,1,1] => 266 [7,6,4] => 225 [7,6,3,1] => 389 [7,6,2,2] => 358 [7,6,2,1,1] => 446 [7,6,1,1,1,1] => 327 [7,5,5] => 207 [7,5,4,1] => 389 [7,5,3,2] => 436 [7,5,3,1,1] => 517 [7,5,2,2,1] => 515 [7,5,2,1,1,1] => 534 [7,5,1,1,1,1,1] => 367 [7,4,4,2] => 387 [7,4,4,1,1] => 457 [7,4,3,3] => 378 [7,4,3,2,1] => 582 [7,4,3,1,1,1] => 563 [7,4,2,2,2] => 473 [7,4,2,2,1,1] => 594 [7,4,2,1,1,1,1] => 562 [7,4,1,1,1,1,1,1] => 377 [7,3,3,3,1] => 423 [7,3,3,2,2] => 439 [7,3,3,2,1,1] => 549 [7,3,3,1,1,1,1] => 494 [7,3,2,2,2,1] => 507 [7,3,2,2,1,1,1] => 562 [7,3,2,1,1,1,1,1] => 509 [7,3,1,1,1,1,1,1,1] => 348 [7,2,2,2,2,2] => 297 [7,2,2,2,2,1,1] => 367 [7,2,2,2,1,1,1,1] => 386 [7,2,2,1,1,1,1,1,1] => 354 [7,2,1,1,1,1,1,1,1,1] => 271 [7,1,1,1,1,1,1,1,1,1,1] => 137 [6,6,5] => 167 [6,6,4,1] => 313 [6,6,3,2] => 350 [6,6,3,1,1] => 416 [6,6,2,2,1] => 415 [6,6,2,1,1,1] => 431 [6,6,1,1,1,1,1] => 297 [6,5,5,1] => 301 [6,5,4,2] => 370 [6,5,4,1,1] => 433 [6,5,3,3] => 350 [6,5,3,2,1] => 540 [6,5,3,1,1,1] => 518 [6,5,2,2,2] => 428 [6,5,2,2,1,1] => 538 [6,5,2,1,1,1,1] => 507 [6,5,1,1,1,1,1,1] => 335 [6,4,4,3] => 325 [6,4,4,2,1] => 496 [6,4,4,1,1,1] => 472 [6,4,3,3,1] => 493 [6,4,3,2,2] => 506 [6,4,3,2,1,1] => 631 [6,4,3,1,1,1,1] => 549 [6,4,2,2,2,1] => 538 [6,4,2,2,1,1,1] => 594 [6,4,2,1,1,1,1,1] => 530 [6,4,1,1,1,1,1,1,1] => 346 [6,3,3,3,2] => 383 [6,3,3,3,1,1] => 472 [6,3,3,2,2,1] => 518 [6,3,3,2,1,1,1] => 563 [6,3,3,1,1,1,1,1] => 476 [6,3,2,2,2,2] => 431 [6,3,2,2,2,1,1] => 534 [6,3,2,2,1,1,1,1] => 550 [6,3,2,1,1,1,1,1,1] => 479 [6,3,1,1,1,1,1,1,1,1] => 321 [6,2,2,2,2,2,1] => 327 [6,2,2,2,2,1,1,1] => 371 [6,2,2,2,1,1,1,1,1] => 373 [6,2,2,1,1,1,1,1,1,1] => 333 [6,2,1,1,1,1,1,1,1,1,1] => 251 [6,1,1,1,1,1,1,1,1,1,1,1] => 127 [5,5,5,2] => 250 [5,5,5,1,1] => 295 [5,5,4,3] => 265 [5,5,4,2,1] => 405 [5,5,4,1,1,1] => 383 [5,5,3,3,1] => 395 [5,5,3,2,2] => 405 [5,5,3,2,1,1] => 506 [5,5,3,1,1,1,1] => 439 [5,5,2,2,2,1] => 428 [5,5,2,2,1,1,1] => 473 [5,5,2,1,1,1,1,1] => 422 [5,5,1,1,1,1,1,1,1] => 275 [5,4,4,4] => 235 [5,4,4,3,1] => 392 [5,4,4,2,2] => 395 [5,4,4,2,1,1] => 493 [5,4,4,1,1,1,1] => 423 [5,4,3,3,2] => 405 [5,4,3,3,1,1] => 496 [5,4,3,2,2,1] => 540 [5,4,3,2,1,1,1] => 582 [5,4,3,1,1,1,1,1] => 477 [5,4,2,2,2,2] => 415 [5,4,2,2,2,1,1] => 515 [5,4,2,2,1,1,1,1] => 528 [5,4,2,1,1,1,1,1,1] => 454 [5,4,1,1,1,1,1,1,1,1] => 293 [5,3,3,3,3] => 295 [5,3,3,3,2,1] => 433 [5,3,3,3,1,1,1] => 457 [5,3,3,2,2,2] => 416 [5,3,3,2,2,1,1] => 517 [5,3,3,2,1,1,1,1] => 519 [5,3,3,1,1,1,1,1,1] => 422 [5,3,2,2,2,2,1] => 446 [5,3,2,2,2,1,1,1] => 503 [5,3,2,2,1,1,1,1,1] => 494 [5,3,2,1,1,1,1,1,1,1] => 419 [5,3,1,1,1,1,1,1,1,1,1] => 278 [5,2,2,2,2,2,2] => 266 [5,2,2,2,2,2,1,1] => 323 [5,2,2,2,2,1,1,1,1] => 347 [5,2,2,2,1,1,1,1,1,1] => 338 [5,2,2,1,1,1,1,1,1,1,1] => 296 [5,2,1,1,1,1,1,1,1,1,1,1] => 221 [5,1,1,1,1,1,1,1,1,1,1,1,1] => 113 [4,4,4,4,1] => 235 [4,4,4,3,2] => 265 [4,4,4,3,1,1] => 325 [4,4,4,2,2,1] => 350 [4,4,4,2,1,1,1] => 378 [4,4,4,1,1,1,1,1] => 310 [4,4,3,3,3] => 250 [4,4,3,3,2,1] => 370 [4,4,3,3,1,1,1] => 387 [4,4,3,2,2,2] => 350 [4,4,3,2,2,1,1] => 436 [4,4,3,2,1,1,1,1] => 435 [4,4,3,1,1,1,1,1,1] => 347 [4,4,2,2,2,2,1] => 358 [4,4,2,2,2,1,1,1] => 404 [4,4,2,2,1,1,1,1,1] => 396 [4,4,2,1,1,1,1,1,1,1] => 334 [4,4,1,1,1,1,1,1,1,1,1] => 218 [4,3,3,3,3,1] => 301 [4,3,3,3,2,2] => 313 [4,3,3,3,2,1,1] => 389 [4,3,3,3,1,1,1,1] => 378 [4,3,3,2,2,2,1] => 389 [4,3,3,2,2,1,1,1] => 436 [4,3,3,2,1,1,1,1,1] => 417 [4,3,3,1,1,1,1,1,1,1] => 332 [4,3,2,2,2,2,2] => 319 [4,3,2,2,2,2,1,1] => 389 [4,3,2,2,2,1,1,1,1] => 414 [4,3,2,2,1,1,1,1,1,1] => 394 [4,3,2,1,1,1,1,1,1,1,1] => 329 [4,3,1,1,1,1,1,1,1,1,1,1] => 219 [4,2,2,2,2,2,2,1] => 251 [4,2,2,2,2,2,1,1,1] => 285 [4,2,2,2,2,1,1,1,1,1] => 295 [4,2,2,2,1,1,1,1,1,1,1] => 281 [4,2,2,1,1,1,1,1,1,1,1,1] => 243 [4,2,1,1,1,1,1,1,1,1,1,1,1] => 181 [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 95 [3,3,3,3,3,2] => 167 [3,3,3,3,3,1,1] => 207 [3,3,3,3,2,2,1] => 225 [3,3,3,3,2,1,1,1] => 251 [3,3,3,3,1,1,1,1,1] => 235 [3,3,3,2,2,2,2] => 212 [3,3,3,2,2,2,1,1] => 260 [3,3,3,2,2,1,1,1,1] => 275 [3,3,3,2,1,1,1,1,1,1] => 257 [3,3,3,1,1,1,1,1,1,1,1] => 206 [3,3,2,2,2,2,2,1] => 229 [3,3,2,2,2,2,1,1,1] => 260 [3,3,2,2,2,1,1,1,1,1] => 267 [3,3,2,2,1,1,1,1,1,1,1] => 250 [3,3,2,1,1,1,1,1,1,1,1,1] => 209 [3,3,1,1,1,1,1,1,1,1,1,1,1] => 144 [3,2,2,2,2,2,2,2] => 164 [3,2,2,2,2,2,2,1,1] => 196 [3,2,2,2,2,2,1,1,1,1] => 213 [3,2,2,2,2,1,1,1,1,1,1] => 215 [3,2,2,2,1,1,1,1,1,1,1,1] => 202 [3,2,2,1,1,1,1,1,1,1,1,1,1] => 174 ----------------------------------------------------------------------------- Created: Mar 03, 2019 at 21:56 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 03, 2019 at 21:56 by Martin Rubey