***************************************************************************** * 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: St001127 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The sum of the squares of the parts of a partition. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(pi): return sum(p^2 for p in pi) ----------------------------------------------------------------------------- Statistic values: [] => 0 [1] => 1 [2] => 4 [1,1] => 2 [3] => 9 [2,1] => 5 [1,1,1] => 3 [4] => 16 [3,1] => 10 [2,2] => 8 [2,1,1] => 6 [1,1,1,1] => 4 [5] => 25 [4,1] => 17 [3,2] => 13 [3,1,1] => 11 [2,2,1] => 9 [2,1,1,1] => 7 [1,1,1,1,1] => 5 [6] => 36 [5,1] => 26 [4,2] => 20 [4,1,1] => 18 [3,3] => 18 [3,2,1] => 14 [3,1,1,1] => 12 [2,2,2] => 12 [2,2,1,1] => 10 [2,1,1,1,1] => 8 [1,1,1,1,1,1] => 6 [7] => 49 [6,1] => 37 [5,2] => 29 [5,1,1] => 27 [4,3] => 25 [4,2,1] => 21 [4,1,1,1] => 19 [3,3,1] => 19 [3,2,2] => 17 [3,2,1,1] => 15 [3,1,1,1,1] => 13 [2,2,2,1] => 13 [2,2,1,1,1] => 11 [2,1,1,1,1,1] => 9 [1,1,1,1,1,1,1] => 7 [8] => 64 [7,1] => 50 [6,2] => 40 [6,1,1] => 38 [5,3] => 34 [5,2,1] => 30 [5,1,1,1] => 28 [4,4] => 32 [4,3,1] => 26 [4,2,2] => 24 [4,2,1,1] => 22 [4,1,1,1,1] => 20 [3,3,2] => 22 [3,3,1,1] => 20 [3,2,2,1] => 18 [3,2,1,1,1] => 16 [3,1,1,1,1,1] => 14 [2,2,2,2] => 16 [2,2,2,1,1] => 14 [2,2,1,1,1,1] => 12 [2,1,1,1,1,1,1] => 10 [1,1,1,1,1,1,1,1] => 8 [9] => 81 [8,1] => 65 [7,2] => 53 [7,1,1] => 51 [6,3] => 45 [6,2,1] => 41 [6,1,1,1] => 39 [5,4] => 41 [5,3,1] => 35 [5,2,2] => 33 [5,2,1,1] => 31 [5,1,1,1,1] => 29 [4,4,1] => 33 [4,3,2] => 29 [4,3,1,1] => 27 [4,2,2,1] => 25 [4,2,1,1,1] => 23 [4,1,1,1,1,1] => 21 [3,3,3] => 27 [3,3,2,1] => 23 [3,3,1,1,1] => 21 [3,2,2,2] => 21 [3,2,2,1,1] => 19 [3,2,1,1,1,1] => 17 [3,1,1,1,1,1,1] => 15 [2,2,2,2,1] => 17 [2,2,2,1,1,1] => 15 [2,2,1,1,1,1,1] => 13 [2,1,1,1,1,1,1,1] => 11 [1,1,1,1,1,1,1,1,1] => 9 [10] => 100 [9,1] => 82 [8,2] => 68 [8,1,1] => 66 [7,3] => 58 [7,2,1] => 54 [7,1,1,1] => 52 [6,4] => 52 [6,3,1] => 46 [6,2,2] => 44 [6,2,1,1] => 42 [6,1,1,1,1] => 40 [5,5] => 50 [5,4,1] => 42 [5,3,2] => 38 [5,3,1,1] => 36 [5,2,2,1] => 34 [5,2,1,1,1] => 32 [5,1,1,1,1,1] => 30 [4,4,2] => 36 [4,4,1,1] => 34 [4,3,3] => 34 [4,3,2,1] => 30 [4,3,1,1,1] => 28 [4,2,2,2] => 28 [4,2,2,1,1] => 26 [4,2,1,1,1,1] => 24 [4,1,1,1,1,1,1] => 22 [3,3,3,1] => 28 [3,3,2,2] => 26 [3,3,2,1,1] => 24 [3,3,1,1,1,1] => 22 [3,2,2,2,1] => 22 [3,2,2,1,1,1] => 20 [3,2,1,1,1,1,1] => 18 [3,1,1,1,1,1,1,1] => 16 [2,2,2,2,2] => 20 [2,2,2,2,1,1] => 18 [2,2,2,1,1,1,1] => 16 [2,2,1,1,1,1,1,1] => 14 [2,1,1,1,1,1,1,1,1] => 12 [1,1,1,1,1,1,1,1,1,1] => 10 [11] => 121 [10,1] => 101 [9,2] => 85 [9,1,1] => 83 [8,3] => 73 [8,2,1] => 69 [8,1,1,1] => 67 [7,4] => 65 [7,3,1] => 59 [7,2,2] => 57 [7,2,1,1] => 55 [7,1,1,1,1] => 53 [6,5] => 61 [6,4,1] => 53 [6,3,2] => 49 [6,3,1,1] => 47 [6,2,2,1] => 45 [6,2,1,1,1] => 43 [6,1,1,1,1,1] => 41 [5,5,1] => 51 [5,4,2] => 45 [5,4,1,1] => 43 [5,3,3] => 43 [5,3,2,1] => 39 [5,3,1,1,1] => 37 [5,2,2,2] => 37 [5,2,2,1,1] => 35 [5,2,1,1,1,1] => 33 [5,1,1,1,1,1,1] => 31 [4,4,3] => 41 [4,4,2,1] => 37 [4,4,1,1,1] => 35 [4,3,3,1] => 35 [4,3,2,2] => 33 [4,3,2,1,1] => 31 [4,3,1,1,1,1] => 29 [4,2,2,2,1] => 29 [4,2,2,1,1,1] => 27 [4,2,1,1,1,1,1] => 25 [4,1,1,1,1,1,1,1] => 23 [3,3,3,2] => 31 [3,3,3,1,1] => 29 [3,3,2,2,1] => 27 [3,3,2,1,1,1] => 25 [3,3,1,1,1,1,1] => 23 [3,2,2,2,2] => 25 [3,2,2,2,1,1] => 23 [3,2,2,1,1,1,1] => 21 [3,2,1,1,1,1,1,1] => 19 [3,1,1,1,1,1,1,1,1] => 17 [2,2,2,2,2,1] => 21 [2,2,2,2,1,1,1] => 19 [2,2,2,1,1,1,1,1] => 17 [2,2,1,1,1,1,1,1,1] => 15 [2,1,1,1,1,1,1,1,1,1] => 13 [1,1,1,1,1,1,1,1,1,1,1] => 11 [12] => 144 [11,1] => 122 [10,2] => 104 [10,1,1] => 102 [9,3] => 90 [9,2,1] => 86 [9,1,1,1] => 84 [8,4] => 80 [8,3,1] => 74 [8,2,2] => 72 [8,2,1,1] => 70 [8,1,1,1,1] => 68 [7,5] => 74 [7,4,1] => 66 [7,3,2] => 62 [7,3,1,1] => 60 [7,2,2,1] => 58 [7,2,1,1,1] => 56 [7,1,1,1,1,1] => 54 [6,6] => 72 [6,5,1] => 62 [6,4,2] => 56 [6,4,1,1] => 54 [6,3,3] => 54 [6,3,2,1] => 50 [6,3,1,1,1] => 48 [6,2,2,2] => 48 [6,2,2,1,1] => 46 [6,2,1,1,1,1] => 44 [6,1,1,1,1,1,1] => 42 [5,5,2] => 54 [5,5,1,1] => 52 [5,4,3] => 50 [5,4,2,1] => 46 [5,4,1,1,1] => 44 [5,3,3,1] => 44 [5,3,2,2] => 42 [5,3,2,1,1] => 40 [5,3,1,1,1,1] => 38 [5,2,2,2,1] => 38 [5,2,2,1,1,1] => 36 [5,2,1,1,1,1,1] => 34 [5,1,1,1,1,1,1,1] => 32 [4,4,4] => 48 [4,4,3,1] => 42 [4,4,2,2] => 40 [4,4,2,1,1] => 38 [4,4,1,1,1,1] => 36 [4,3,3,2] => 38 [4,3,3,1,1] => 36 [4,3,2,2,1] => 34 [4,3,2,1,1,1] => 32 [4,3,1,1,1,1,1] => 30 [4,2,2,2,2] => 32 [4,2,2,2,1,1] => 30 [4,2,2,1,1,1,1] => 28 [4,2,1,1,1,1,1,1] => 26 [4,1,1,1,1,1,1,1,1] => 24 [3,3,3,3] => 36 [3,3,3,2,1] => 32 [3,3,3,1,1,1] => 30 [3,3,2,2,2] => 30 [3,3,2,2,1,1] => 28 [3,3,2,1,1,1,1] => 26 [3,3,1,1,1,1,1,1] => 24 [3,2,2,2,2,1] => 26 [3,2,2,2,1,1,1] => 24 [3,2,2,1,1,1,1,1] => 22 [3,2,1,1,1,1,1,1,1] => 20 [3,1,1,1,1,1,1,1,1,1] => 18 [2,2,2,2,2,2] => 24 [2,2,2,2,2,1,1] => 22 [2,2,2,2,1,1,1,1] => 20 [2,2,2,1,1,1,1,1,1] => 18 [2,2,1,1,1,1,1,1,1,1] => 16 [2,1,1,1,1,1,1,1,1,1,1] => 14 [1,1,1,1,1,1,1,1,1,1,1,1] => 12 [5,4,3,1] => 51 [5,4,2,2] => 49 [5,4,2,1,1] => 47 [5,3,3,2] => 47 [5,3,3,1,1] => 45 [5,3,2,2,1] => 43 [4,4,3,2] => 45 [4,4,3,1,1] => 43 [4,4,2,2,1] => 41 [4,3,3,2,1] => 39 [5,4,3,2] => 54 [5,4,3,1,1] => 52 [5,4,2,2,1] => 50 [5,3,3,2,1] => 48 [4,4,3,2,1] => 46 [5,4,3,2,1] => 55 ----------------------------------------------------------------------------- Created: Mar 20, 2018 at 16:22 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 26, 2018 at 07:41 by Martin Rubey