***************************************************************************** * 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: St001899 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The total number of irreducible representations contained in the higher Lie character for an integer partition. ----------------------------------------------------------------------------- References: [1] (service unreachable) [[MathSciNet:1984625]] ----------------------------------------------------------------------------- Code: def statistic(la): s = SymmetricFunctions(ZZ).s() return sum(c for _, c in s.higher_lie_character(la)) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 1 [1,1] => 1 [3] => 1 [2,1] => 2 [1,1,1] => 1 [4] => 2 [3,1] => 3 [2,2] => 2 [2,1,1] => 2 [1,1,1,1] => 1 [5] => 5 [4,1] => 6 [3,2] => 4 [3,1,1] => 4 [2,2,1] => 4 [2,1,1,1] => 2 [1,1,1,1,1] => 1 [6] => 12 [5,1] => 15 [4,2] => 9 [4,1,1] => 9 [3,3] => 4 [3,2,1] => 12 [3,1,1,1] => 4 [2,2,2] => 3 [2,2,1,1] => 5 [2,1,1,1,1] => 2 [1,1,1,1,1,1] => 1 [7] => 33 [6,1] => 38 [5,2] => 23 [5,1,1] => 23 [4,3] => 18 [4,2,1] => 28 [4,1,1,1] => 10 [3,3,1] => 12 [3,2,2] => 10 [3,2,1,1] => 18 [3,1,1,1,1] => 4 [2,2,2,1] => 7 [2,2,1,1,1] => 5 [2,1,1,1,1,1] => 2 [1,1,1,1,1,1,1] => 1 [8] => 94 [7,1] => 109 [6,2] => 64 [6,1,1] => 62 [5,3] => 49 [5,2,1] => 76 [5,1,1,1] => 27 [4,4] => 24 [4,3,1] => 60 [4,2,2] => 24 [4,2,1,1] => 46 [4,1,1,1,1] => 10 [3,3,2] => 19 [3,3,1,1] => 21 [3,2,2,1] => 33 [3,2,1,1,1] => 20 [3,1,1,1,1,1] => 4 [2,2,2,2] => 5 [2,2,2,1,1] => 9 [2,2,1,1,1,1] => 5 [2,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1] => 1 [9] => 290 [8,1] => 326 [7,2] => 187 [7,1,1] => 187 [6,3] => 141 [6,2,1] => 218 [6,1,1,1] => 75 [5,4] => 128 [5,3,1] => 169 [5,2,2] => 69 [5,2,1,1] => 128 [5,1,1,1,1] => 28 [4,4,1] => 80 [4,3,2] => 104 [4,3,1,1] => 104 [4,2,2,1] => 84 [4,2,1,1,1] => 54 [4,1,1,1,1,1] => 10 [3,3,3] => 16 [3,3,2,1] => 68 [3,3,1,1,1] => 25 [3,2,2,2] => 21 [3,2,2,1,1] => 54 [3,2,1,1,1,1] => 20 [3,1,1,1,1,1,1] => 4 [2,2,2,2,1] => 12 [2,2,2,1,1,1] => 10 [2,2,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1] => 1 [10] => 949 [9,1] => 1054 [8,2] => 592 [8,1,1] => 592 [7,3] => 441 [7,2,1] => 678 [7,1,1,1] => 237 [6,4] => 388 [6,3,1] => 513 [6,2,2] => 207 [6,2,1,1] => 388 [6,1,1,1,1] => 80 [5,5] => 189 [5,4,1] => 466 [5,3,2] => 308 [5,3,1,1] => 308 [5,2,2,1] => 248 [5,2,1,1,1] => 158 [5,1,1,1,1,1] => 28 [4,4,2] => 145 [4,4,1,1] => 145 [4,3,3] => 124 [4,3,2,1] => 380 [4,3,1,1,1] => 132 [4,2,2,2] => 56 [4,2,2,1,1] => 148 [4,2,1,1,1,1] => 56 [4,1,1,1,1,1,1] => 10 [3,3,3,1] => 56 [3,3,2,2] => 65 [3,3,2,1,1] => 124 [3,3,1,1,1,1] => 26 [3,2,2,2,1] => 75 [3,2,2,1,1,1] => 64 [3,2,1,1,1,1,1] => 20 [3,1,1,1,1,1,1,1] => 4 [2,2,2,2,2] => 7 [2,2,2,2,1,1] => 17 [2,2,2,1,1,1,1] => 10 [2,2,1,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1] => 1 [11] => 3245 [10,1] => 3569 [9,2] => 1982 [9,1,1] => 1982 [8,3] => 1454 [8,2,1] => 2228 [8,1,1,1] => 774 [7,4] => 1258 [7,3,1] => 1663 [7,2,2] => 662 [7,2,1,1] => 1258 [7,1,1,1,1] => 257 [6,5] => 1184 [6,4,1] => 1464 [6,3,2] => 969 [6,3,1,1] => 967 [6,2,2,1] => 772 [6,2,1,1,1] => 495 [6,1,1,1,1,1] => 81 [5,5,1] => 711 [5,4,2] => 879 [5,4,1,1] => 879 [5,3,3] => 380 [5,3,2,1] => 1162 [5,3,1,1,1] => 402 [5,2,2,2] => 169 [5,2,2,1,1] => 451 [5,2,1,1,1,1] => 168 [5,1,1,1,1,1,1] => 28 [4,4,3] => 356 [4,4,2,1] => 546 [4,4,1,1,1] => 190 [4,3,3,1] => 470 [4,3,2,2] => 372 [4,3,2,1,1] => 710 [4,3,1,1,1,1] => 142 [4,2,2,2,1] => 207 [4,2,2,1,1,1] => 185 [4,2,1,1,1,1,1] => 56 [4,1,1,1,1,1,1,1] => 10 [3,3,3,2] => 104 [3,3,3,1,1] => 106 [3,3,2,2,1] => 245 [3,3,2,1,1,1] => 159 [3,3,1,1,1,1,1] => 26 [3,2,2,2,2] => 41 [3,2,2,2,1,1] => 132 [3,2,2,1,1,1,1] => 66 [3,2,1,1,1,1,1,1] => 20 [3,1,1,1,1,1,1,1,1] => 4 [2,2,2,2,2,1] => 19 [2,2,2,2,1,1,1] => 19 [2,2,2,1,1,1,1,1] => 10 [2,2,1,1,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1] => 1 [12] => 11666 [11,1] => 12741 [10,2] => 7013 [10,1,1] => 7001 [9,3] => 5094 [9,2,1] => 7784 [9,1,1,1] => 2690 [8,4] => 4332 [8,3,1] => 5726 [8,2,2] => 2254 [8,2,1,1] => 4332 [8,1,1,1,1] => 860 [7,5] => 3997 [7,4,1] => 4950 [7,3,2] => 3274 [7,3,1,1] => 3274 [7,2,2,1] => 2584 [7,2,1,1,1] => 1676 [7,1,1,1,1,1] => 263 [6,6] => 1950 [6,5,1] => 4654 [6,4,2] => 2882 [6,4,1,1] => 2882 [6,3,3] => 1246 [6,3,2,1] => 3816 [6,3,1,1,1] => 1311 [6,2,2,2] => 544 [6,2,2,1,1] => 1470 [6,2,1,1,1,1] => 541 [6,1,1,1,1,1,1] => 81 [5,5,2] => 1391 [5,5,1,1] => 1403 [5,4,3] => 2264 [5,4,2,1] => 3460 [5,4,1,1,1] => 1196 [5,3,3,1] => 1500 [5,3,2,2] => 1181 [5,3,2,1,1] => 2264 [5,3,1,1,1,1] => 445 [5,2,2,2,1] => 650 [5,2,2,1,1,1] => 587 [5,2,1,1,1,1,1] => 170 [5,1,1,1,1,1,1,1] => 28 [4,4,4] => 356 [4,4,3,1] => 1406 [4,4,2,2] => 559 [4,4,2,1,1] => 1060 [4,4,1,1,1,1] => 213 [4,3,3,2] => 929 [4,3,3,1,1] => 929 [4,3,2,2,1] => 1460 [4,3,2,1,1,1] => 948 [4,3,1,1,1,1,1] => 144 [4,2,2,2,2] => 114 [4,2,2,2,1,1] => 389 [4,2,2,1,1,1,1] => 197 [4,2,1,1,1,1,1,1] => 56 [4,1,1,1,1,1,1,1,1] => 10 [3,3,3,3] => 69 [3,3,3,2,1] => 410 [3,3,3,1,1,1] => 146 [3,3,2,2,2] => 170 [3,3,2,2,1,1] => 477 [3,3,2,1,1,1,1] => 171 [3,3,1,1,1,1,1,1] => 26 [3,2,2,2,2,1] => 154 [3,2,2,2,1,1,1] => 165 [3,2,2,1,1,1,1,1] => 66 [3,2,1,1,1,1,1,1,1] => 20 [3,1,1,1,1,1,1,1,1,1] => 4 [2,2,2,2,2,2] => 11 [2,2,2,2,2,1,1] => 28 [2,2,2,2,1,1,1,1] => 20 [2,2,2,1,1,1,1,1,1] => 10 [2,2,1,1,1,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1] => 1 [13] => 43731 [12,1] => 47362 [11,2] => 25841 [11,1,1] => 25841 [10,3] => 18633 [10,2,1] => 28430 [10,1,1,1] => 9785 [9,4] => 15644 [9,3,1] => 20702 [9,2,2] => 8112 [9,2,1,1] => 15644 [9,1,1,1,1] => 3054 [8,5] => 14186 [8,4,1] => 17596 [8,3,2] => 11640 [8,3,1,1] => 11640 [8,2,2,1] => 9118 [8,2,1,1,1] => 5956 [8,1,1,1,1,1] => 888 [7,6] => 13512 [7,5,1] => 16219 [7,4,2] => 10057 [7,4,1,1] => 10057 [7,3,3] => 4368 [7,3,2,1] => 13308 [7,3,1,1,1] => 4572 [7,2,2,2] => 1854 [7,2,2,1,1] => 5122 [7,2,1,1,1,1] => 1871 [7,1,1,1,1,1,1] => 264 [6,6,1] => 7882 [6,5,2] => 9452 [6,5,1,1] => 9442 [6,4,3] => 7682 [6,4,2,1] => 11720 [6,4,1,1,1] => 4030 [6,3,3,1] => 5086 [6,3,2,2] => 3986 [6,3,2,1,1] => 7682 [6,3,1,1,1,1] => 1481 [6,2,2,2,1] => 2164 [6,2,2,1,1,1] => 1980 [6,2,1,1,1,1,1] => 553 [6,1,1,1,1,1,1,1] => 81 [5,5,3] => 3717 [5,5,2,1] => 5664 [5,5,1,1,1] => 1959 [5,4,4] => 3490 [5,4,3,1] => 9220 [5,4,2,2] => 3608 [5,4,2,1,1] => 6970 [5,4,1,1,1,1] => 1358 [5,3,3,2] => 3049 [5,3,3,1,1] => 3059 [5,3,2,2,1] => 4779 [5,3,2,1,1,1] => 3112 [5,3,1,1,1,1,1] => 457 [5,2,2,2,2] => 367 [5,2,2,2,1,1] => 1259 [5,2,2,1,1,1,1] => 643 [5,2,1,1,1,1,1,1] => 170 [5,1,1,1,1,1,1,1,1] => 28 [4,4,4,1] => 1448 [4,4,3,2] => 2864 [4,4,3,1,1] => 2864 [4,4,2,2,1] => 2245 [4,4,2,1,1,1] => 1464 [4,4,1,1,1,1,1] => 219 [4,3,3,3] => 832 [4,3,3,2,1] => 3784 [4,3,3,1,1,1] => 1302 [4,3,2,2,2] => 1048 [4,3,2,2,1,1] => 2910 [4,3,2,1,1,1,1] => 1054 [4,3,1,1,1,1,1,1] => 144 [4,2,2,2,2,1] => 450 [4,2,2,2,1,1,1] => 511 [4,2,2,1,1,1,1,1] => 199 [4,2,1,1,1,1,1,1,1] => 56 [4,1,1,1,1,1,1,1,1,1] => 10 [3,3,3,3,1] => 279 [3,3,3,2,2] => 428 [3,3,3,2,1,1] => 832 [3,3,3,1,1,1,1] => 164 [3,3,2,2,2,1] => 690 [3,3,2,2,1,1,1] => 643 [3,3,2,1,1,1,1,1] => 173 [3,3,1,1,1,1,1,1,1] => 26 [3,2,2,2,2,2] => 74 [3,2,2,2,2,1,1] => 287 [3,2,2,2,1,1,1,1] => 176 [3,2,2,1,1,1,1,1,1] => 66 [3,2,1,1,1,1,1,1,1,1] => 20 [3,1,1,1,1,1,1,1,1,1,1] => 4 [2,2,2,2,2,2,1] => 30 [2,2,2,2,2,1,1,1] => 33 [2,2,2,2,1,1,1,1,1] => 20 [2,2,2,1,1,1,1,1,1,1] => 10 [2,2,1,1,1,1,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [14] => 170748 [13,1] => 183883 [12,2] => 99590 [12,1,1] => 99590 [11,3] => 71357 [11,2,1] => 108658 [11,1,1,1] => 37301 [10,4] => 59286 [10,3,1] => 78491 [10,2,2] => 30598 [10,2,1,1] => 59286 [10,1,1,1,1] => 11381 [9,5] => 53058 [9,4,1] => 65868 [9,3,2] => 43604 [9,3,1,1] => 43604 [9,2,2,1] => 33988 [9,2,1,1,1] => 22264 [9,1,1,1,1,1] => 3194 [8,6] => 49720 [8,5,1] => 59674 [8,4,2] => 37044 [8,4,1,1] => 37044 [8,3,3] => 16120 [8,3,2,1] => 49040 [8,3,1,1,1] => 16800 [8,2,2,2] => 6725 [8,2,2,1,1] => 18815 [8,2,1,1,1,1] => 6819 [8,1,1,1,1,1,1] => 895 [7,7] => 24388 [7,6,1] => 56838 [7,5,2] => 34109 [7,5,1,1] => 34109 [7,4,3] => 27810 [7,4,2,1] => 42344 [7,4,1,1,1] => 14534 [7,3,3,1] => 18428 [7,3,2,2] => 14346 [7,3,2,1,1] => 27810 [7,3,1,1,1,1] => 5300 [7,2,2,2,1] => 7695 [7,2,2,1,1,1] => 7165 [7,2,1,1,1,1,1] => 1936 [7,1,1,1,1,1,1,1] => 264 [6,6,2] => 16582 [6,6,1,1] => 16558 [6,5,3] => 26105 [6,5,2,1] => 39762 [6,5,1,1,1] => 13627 [6,4,4] => 12254 [6,4,3,1] => 32410 [6,4,2,2] => 12625 [6,4,2,1,1] => 24484 [6,4,1,1,1,1] => 4685 [6,3,3,2] => 10727 [6,3,3,1,1] => 10743 [6,3,2,2,1] => 16730 [6,3,2,1,1,1] => 10925 [6,3,1,1,1,1,1] => 1542 [6,2,2,2,2] => 1247 [6,2,2,2,1,1] => 4374 [6,2,2,1,1,1,1] => 2228 [6,2,1,1,1,1,1,1] => 555 [6,1,1,1,1,1,1,1,1] => 81 [5,5,4] => 11832 [5,5,3,1] => 15665 [5,5,2,2] => 6099 [5,5,2,1,1] => 11832 [5,5,1,1,1,1] => 2278 [5,4,4,1] => 14708 [5,4,3,2] => 19448 [5,4,3,1,1] => 19448 [5,4,2,2,1] => 15144 [5,4,2,1,1,1] => 9938 [5,4,1,1,1,1,1] => 1418 [5,3,3,3] => 2832 [5,3,3,2,1] => 12872 [5,3,3,1,1,1] => 4421 [5,3,2,2,2] => 3529 [5,3,2,2,1,1] => 9878 [5,3,2,1,1,1,1] => 3552 [5,3,1,1,1,1,1,1] => 459 [5,2,2,2,2,1] => 1493 [5,2,2,2,1,1,1] => 1720 [5,2,2,1,1,1,1,1] => 658 [5,2,1,1,1,1,1,1,1] => 170 [5,1,1,1,1,1,1,1,1,1] => 28 [4,4,4,2] => 3051 [4,4,4,1,1] => 3051 [4,4,3,3] => 3974 [4,4,3,2,1] => 12088 [4,4,3,1,1,1] => 4140 [4,4,2,2,2] => 1657 [4,4,2,2,1,1] => 4637 [4,4,2,1,1,1,1] => 1680 [4,4,1,1,1,1,1,1] => 220 [4,3,3,3,1] => 3516 [4,3,3,2,2] => 4083 [4,3,3,2,1,1] => 7940 [4,3,3,1,1,1,1] => 1507 [4,3,2,2,2,1] => 4370 [4,3,2,2,1,1,1] => 4080 [4,3,2,1,1,1,1,1] => 1084 [4,3,1,1,1,1,1,1,1] => 144 [4,2,2,2,2,2] => 218 [4,2,2,2,2,1,1] => 890 [4,2,2,2,1,1,1,1] => 563 [4,2,2,1,1,1,1,1,1] => 199 [4,2,1,1,1,1,1,1,1,1] => 56 [4,1,1,1,1,1,1,1,1,1,1] => 10 [3,3,3,3,2] => 583 [3,3,3,3,1,1] => 591 [3,3,3,2,2,1] => 1802 [3,3,3,2,1,1,1] => 1191 [3,3,3,1,1,1,1,1] => 169 [3,3,2,2,2,2] => 396 [3,3,2,2,2,1,1] => 1414 [3,3,2,2,1,1,1,1] => 718 [3,3,2,1,1,1,1,1,1] => 173 [3,3,1,1,1,1,1,1,1,1] => 26 [3,2,2,2,2,2,1] => 292 [3,2,2,2,2,1,1,1] => 377 [3,2,2,2,1,1,1,1,1] => 178 [3,2,2,1,1,1,1,1,1,1] => 66 [3,2,1,1,1,1,1,1,1,1,1] => 20 [3,1,1,1,1,1,1,1,1,1,1,1] => 4 [2,2,2,2,2,2,2] => 15 [2,2,2,2,2,2,1,1] => 47 [2,2,2,2,2,1,1,1,1] => 35 [2,2,2,2,1,1,1,1,1,1] => 20 [2,2,2,1,1,1,1,1,1,1,1] => 10 [2,2,1,1,1,1,1,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [15] => 689957 [14,1] => 739252 [13,2] => 398059 [13,1,1] => 398059 [12,3] => 283584 [12,2,1] => 431204 [12,1,1,1] => 147620 [11,4] => 233594 [11,3,1] => 309375 [11,2,2] => 120042 [11,2,1,1] => 233594 [11,1,1,1,1] => 44261 [10,5] => 206798 [10,4,1] => 256950 [10,3,2] => 170160 [10,3,1,1] => 170148 [10,2,2,1] => 132056 [10,2,1,1,1] => 86790 [10,1,1,1,1,1] => 12036 [9,6] => 191453 [9,5,1] => 229762 [9,4,2] => 142742 [9,4,1,1] => 142742 [9,3,3] => 62217 [9,3,2,1] => 189052 [9,3,1,1,1] => 64618 [9,2,2,2] => 25633 [9,2,2,1,1] => 72362 [9,2,1,1,1,1] => 26052 [9,1,1,1,1,1,1] => 3231 [8,7] => 184750 [8,6,1] => 215340 [8,5,2] => 129216 [8,5,1,1] => 129216 [8,4,3] => 105596 [8,4,2,1] => 160560 [8,4,1,1,1] => 54964 [8,3,3,1] => 69980 [8,3,2,2] => 54246 [8,3,2,1,1] => 105596 [8,3,1,1,1,1] => 19882 [8,2,2,2,1] => 28824 [8,2,2,1,1,1] => 27142 [8,2,1,1,1,1,1] => 7136 [8,1,1,1,1,1,1,1] => 896 [7,7,1] => 105592 [7,6,2] => 123108 [7,6,1,1] => 123042 [7,5,3] => 97137 [7,5,2,1] => 147704 [7,5,1,1,1] => 50567 [7,4,4] => 45608 [7,4,3,1] => 120700 [7,4,2,2] => 46800 [7,4,2,1,1] => 91150 [7,4,1,1,1,1] => 17250 [7,3,3,2] => 39963 [7,3,3,1,1] => 40029 [7,3,2,2,1] => 62013 [7,3,2,1,1,1] => 40708 [7,3,1,1,1,1,1] => 5584 [7,2,2,2,2] => 4499 [7,2,2,2,1,1] => 16133 [7,2,2,1,1,1,1] => 8253 [7,2,1,1,1,1,1,1] => 1950 [7,1,1,1,1,1,1,1,1] => 264 [6,6,3] => 47187 [6,6,2,1] => 71788 [6,6,1,1,1] => 24525 [6,5,4] => 85488 [6,5,3,1] => 113227 [6,5,2,2] => 43951 [6,5,2,1,1] => 85488 [6,5,1,1,1,1] => 16166 [6,4,4,1] => 53160 [6,4,3,2] => 70363 [6,4,3,1,1] => 70331 [6,4,2,2,1] => 54572 [6,4,2,1,1,1] => 35881 [6,4,1,1,1,1,1] => 4949 [6,3,3,3] => 10244 [6,3,3,2,1] => 46590 [6,3,3,1,1,1] => 15932 [6,3,2,2,2] => 12633 [6,3,2,2,1,1] => 35663 [6,3,2,1,1,1,1] => 12745 [6,3,1,1,1,1,1,1] => 1556 [6,2,2,2,2,1] => 5251 [6,2,2,2,1,1,1] => 6175 [6,2,2,1,1,1,1,1] => 2308 [6,2,1,1,1,1,1,1,1] => 555 [6,1,1,1,1,1,1,1,1,1] => 81 [5,5,5] => 13773 [5,5,4,1] => 51298 [5,5,3,2] => 33964 [5,5,3,1,1] => 33976 [5,5,2,2,1] => 26348 [5,5,2,1,1,1] => 17334 [5,5,1,1,1,1,1] => 2408 [5,4,4,2] => 31899 [5,4,4,1,1] => 31899 [5,4,3,3] => 27784 [5,4,3,2,1] => 84420 [5,4,3,1,1,1] => 28852 [5,4,2,2,2] => 11424 [5,4,2,2,1,1] => 32304 [5,4,2,1,1,1,1] => 11636 [5,4,1,1,1,1,1,1] => 1432 [5,3,3,3,1] => 12300 [5,3,3,2,2] => 14249 [5,3,3,2,1,1] => 27784 [5,3,3,1,1,1,1] => 5224 [5,3,2,2,2,1] => 15146 [5,3,2,2,1,1,1] => 14247 [5,3,2,1,1,1,1,1] => 3703 [5,3,1,1,1,1,1,1,1] => 459 [5,2,2,2,2,2] => 731 [5,2,2,2,2,1,1] => 3050 [5,2,2,2,1,1,1,1] => 1945 [5,2,2,1,1,1,1,1,1] => 660 [5,2,1,1,1,1,1,1,1,1] => 170 [5,1,1,1,1,1,1,1,1,1,1] => 28 [4,4,4,3] => 8702 [4,4,4,2,1] => 13236 [4,4,4,1,1,1] => 4534 [4,4,3,3,1] => 17278 [4,4,3,2,2] => 13383 [4,4,3,2,1,1] => 26076 [4,4,3,1,1,1,1] => 4903 [4,4,2,2,2,1] => 7104 [4,4,2,2,1,1,1] => 6705 [4,4,2,1,1,1,1,1] => 1757 [4,4,1,1,1,1,1,1,1] => 220 [4,3,3,3,2] => 7626 [4,3,3,3,1,1] => 7658 [4,3,3,2,2,1] => 17700 [4,3,3,2,1,1,1] => 11649 [4,3,3,1,1,1,1,1] => 1581 [4,3,2,2,2,2] => 2553 [4,3,2,2,2,1,1] => 9204 [4,3,2,2,1,1,1,1] => 4689 [4,3,2,1,1,1,1,1,1] => 1088 [4,3,1,1,1,1,1,1,1,1] => 144 [4,2,2,2,2,2,1] => 899 [4,2,2,2,2,1,1,1] => 1226 [4,2,2,2,1,1,1,1,1] => 576 [4,2,2,1,1,1,1,1,1,1] => 199 [4,2,1,1,1,1,1,1,1,1,1] => 56 [4,1,1,1,1,1,1,1,1,1,1,1] => 10 [3,3,3,3,3] => 340 [3,3,3,3,2,1] => 2534 [3,3,3,3,1,1,1] => 879 [3,3,3,2,2,2] => 1361 [3,3,3,2,2,1,1] => 3868 [3,3,3,2,1,1,1,1] => 1387 [3,3,3,1,1,1,1,1,1] => 170 [3,3,2,2,2,2,1] => 1685 [3,3,2,2,2,1,1,1] => 2005 [3,3,2,2,1,1,1,1,1] => 737 [3,3,2,1,1,1,1,1,1,1] => 173 [3,3,1,1,1,1,1,1,1,1,1] => 26 [3,2,2,2,2,2,2] => 127 [3,2,2,2,2,2,1,1] => 572 [3,2,2,2,2,1,1,1,1] => 415 [3,2,2,2,1,1,1,1,1,1] => 178 [3,2,2,1,1,1,1,1,1,1,1] => 66 [3,2,1,1,1,1,1,1,1,1,1,1] => 20 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 4 [2,2,2,2,2,2,2,1] => 45 [2,2,2,2,2,2,1,1,1] => 57 [2,2,2,2,2,1,1,1,1,1] => 36 [2,2,2,2,1,1,1,1,1,1,1] => 20 [2,2,2,1,1,1,1,1,1,1,1,1] => 10 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [16] => 2887816 [15,1] => 3080437 [14,2] => 1650300 [14,1,1] => 1650180 [13,3] => 1170211 [13,2,1] => 1777182 [13,1,1,1] => 606971 [12,4] => 956804 [12,3,1] => 1267692 [12,2,2] => 490008 [12,2,1,1] => 956804 [12,1,1,1,1] => 179120 [11,5] => 839473 [11,4,1] => 1043782 [11,3,2] => 691488 [11,3,1,1] => 691488 [11,2,2,1] => 534632 [11,2,1,1,1] => 352294 [11,1,1,1,1,1] => 47453 [10,6] => 769500 [10,5,1] => 923412 [10,4,2] => 574069 [10,4,1,1] => 574081 [10,3,3] => 250568 [10,3,2,1] => 760648 [10,3,1,1,1] => 259420 [10,2,2,2] => 102183 [10,2,2,1,1] => 290517 [10,2,1,1,1,1] => 103986 [10,1,1,1,1,1,1] => 12244 [9,7] => 733362 [9,6,1] => 854937 [9,5,2] => 512986 [9,5,1,1] => 512986 [9,4,3] => 420012 [9,4,2,1] => 637836 [9,4,1,1,1] => 217824 [9,3,3,1] => 278433 [9,3,2,2] => 215100 [9,3,2,1,1] => 420012 [9,3,1,1,1,1] => 78246 [9,2,2,2,1] => 113493 [9,2,2,1,1,1] => 107710 [9,2,1,1,1,1,1] => 27648 [9,1,1,1,1,1,1,1] => 3239 [8,8] => 360962 [8,7,1] => 824910 [8,6,2] => 480908 [8,6,1,1] => 480752 [8,5,3] => 379954 [8,5,2,1] => 577024 [8,5,1,1,1] => 197070 [8,4,4] => 178378 [8,4,3,1] => 472452 [8,4,2,2] => 182552 [8,4,2,1,1] => 356616 [8,4,1,1,1,1] => 66716 [8,3,3,2] => 156516 [8,3,3,1,1] => 156672 [8,3,2,2,1] => 241934 [8,3,2,1,1,1] => 159264 [8,3,1,1,1,1,1] => 21244 [8,2,2,2,2] => 17188 [8,2,2,2,1,1] => 62660 [8,2,2,1,1,1,1] => 32046 [8,2,1,1,1,1,1,1] => 7224 [8,1,1,1,1,1,1,1,1] => 896 [7,7,2] => 235662 [7,7,1,1] => 235782 [7,6,3] => 361905 [7,6,2,1] => 549706 [7,6,1,1,1] => 187583 [7,5,4] => 327776 [7,5,3,1] => 434293 [7,5,2,2] => 167885 [7,5,2,1,1] => 327776 [7,5,1,1,1,1] => 61368 [7,4,4,1] => 203916 [7,4,3,2] => 270004 [7,4,3,1,1] => 270004 [7,4,2,2,1] => 208648 [7,4,2,1,1,1] => 137610 [7,4,1,1,1,1,1] => 18482 [7,3,3,3] => 39372 [7,3,3,2,1] => 178880 [7,3,3,1,1,1] => 61081 [7,3,2,2,2] => 48012 [7,3,2,2,1,1] => 136639 [7,3,2,1,1,1,1] => 48665 [7,3,1,1,1,1,1,1] => 5667 [7,2,2,2,2,1] => 19671 [7,2,2,2,1,1,1] => 23603 [7,2,2,1,1,1,1,1] => 8666 [7,2,1,1,1,1,1,1,1] => 1952 [7,1,1,1,1,1,1,1,1,1] => 264 [6,6,4] => 159196 [6,6,3,1] => 210993 [6,6,2,2] => 81682 [6,6,2,1,1] => 159196 [6,6,1,1,1,1] => 29757 [6,5,5] => 153632 [6,5,4,1] => 382116 [6,5,3,2] => 253203 [6,5,3,1,1] => 253105 [6,5,2,2,1] => 195788 [6,5,2,1,1,1] => 128913 [6,5,1,1,1,1,1] => 17327 [6,4,4,2] => 118900 [6,4,4,1,1] => 118822 [6,4,3,3] => 103716 [6,4,3,2,1] => 314832 [6,4,3,1,1,1] => 107298 [6,4,2,2,2] => 42223 [6,4,2,2,1,1] => 120232 [6,4,2,1,1,1,1] => 42991 [6,4,1,1,1,1,1,1] => 5030 [6,3,3,3,1] => 45890 [6,3,3,2,2] => 53041 [6,3,3,2,1,1] => 103716 [6,3,3,1,1,1,1] => 19259 [6,3,2,2,2,1] => 56007 [6,3,2,2,1,1,1] => 53063 [6,3,2,1,1,1,1,1] => 13479 [6,3,1,1,1,1,1,1,1] => 1558 [6,2,2,2,2,2] => 2612 [6,2,2,2,2,1,1] => 11158 [6,2,2,2,1,1,1,1] => 7171 [6,2,2,1,1,1,1,1,1] => 2325 ----------------------------------------------------------------------------- Created: May 25, 2023 at 14:31 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: May 25, 2023 at 14:31 by Martin Rubey