***************************************************************************** * 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: St000150 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The floored half-sum of the multiplicities of a partition. This statistic is equidistributed with [[St000143]] and [[St000149]], see [1]. ----------------------------------------------------------------------------- References: [1] Tim Statistics on partitions equidistributed with number of even parts [[MathOverflow:134577]] ----------------------------------------------------------------------------- Code: def statistic(L): return sum(e // 2 for e in L.to_exp()) ----------------------------------------------------------------------------- Statistic values: [] => 0 [1] => 0 [2] => 0 [1,1] => 1 [3] => 0 [2,1] => 0 [1,1,1] => 1 [4] => 0 [3,1] => 0 [2,2] => 1 [2,1,1] => 1 [1,1,1,1] => 2 [5] => 0 [4,1] => 0 [3,2] => 0 [3,1,1] => 1 [2,2,1] => 1 [2,1,1,1] => 1 [1,1,1,1,1] => 2 [6] => 0 [5,1] => 0 [4,2] => 0 [4,1,1] => 1 [3,3] => 1 [3,2,1] => 0 [3,1,1,1] => 1 [2,2,2] => 1 [2,2,1,1] => 2 [2,1,1,1,1] => 2 [1,1,1,1,1,1] => 3 [7] => 0 [6,1] => 0 [5,2] => 0 [5,1,1] => 1 [4,3] => 0 [4,2,1] => 0 [4,1,1,1] => 1 [3,3,1] => 1 [3,2,2] => 1 [3,2,1,1] => 1 [3,1,1,1,1] => 2 [2,2,2,1] => 1 [2,2,1,1,1] => 2 [2,1,1,1,1,1] => 2 [1,1,1,1,1,1,1] => 3 [8] => 0 [7,1] => 0 [6,2] => 0 [6,1,1] => 1 [5,3] => 0 [5,2,1] => 0 [5,1,1,1] => 1 [4,4] => 1 [4,3,1] => 0 [4,2,2] => 1 [4,2,1,1] => 1 [4,1,1,1,1] => 2 [3,3,2] => 1 [3,3,1,1] => 2 [3,2,2,1] => 1 [3,2,1,1,1] => 1 [3,1,1,1,1,1] => 2 [2,2,2,2] => 2 [2,2,2,1,1] => 2 [2,2,1,1,1,1] => 3 [2,1,1,1,1,1,1] => 3 [1,1,1,1,1,1,1,1] => 4 [9] => 0 [8,1] => 0 [7,2] => 0 [7,1,1] => 1 [6,3] => 0 [6,2,1] => 0 [6,1,1,1] => 1 [5,4] => 0 [5,3,1] => 0 [5,2,2] => 1 [5,2,1,1] => 1 [5,1,1,1,1] => 2 [4,4,1] => 1 [4,3,2] => 0 [4,3,1,1] => 1 [4,2,2,1] => 1 [4,2,1,1,1] => 1 [4,1,1,1,1,1] => 2 [3,3,3] => 1 [3,3,2,1] => 1 [3,3,1,1,1] => 2 [3,2,2,2] => 1 [3,2,2,1,1] => 2 [3,2,1,1,1,1] => 2 [3,1,1,1,1,1,1] => 3 [2,2,2,2,1] => 2 [2,2,2,1,1,1] => 2 [2,2,1,1,1,1,1] => 3 [2,1,1,1,1,1,1,1] => 3 [1,1,1,1,1,1,1,1,1] => 4 [10] => 0 [9,1] => 0 [8,2] => 0 [8,1,1] => 1 [7,3] => 0 [7,2,1] => 0 [7,1,1,1] => 1 [6,4] => 0 [6,3,1] => 0 [6,2,2] => 1 [6,2,1,1] => 1 [6,1,1,1,1] => 2 [5,5] => 1 [5,4,1] => 0 [5,3,2] => 0 [5,3,1,1] => 1 [5,2,2,1] => 1 [5,2,1,1,1] => 1 [5,1,1,1,1,1] => 2 [4,4,2] => 1 [4,4,1,1] => 2 [4,3,3] => 1 [4,3,2,1] => 0 [4,3,1,1,1] => 1 [4,2,2,2] => 1 [4,2,2,1,1] => 2 [4,2,1,1,1,1] => 2 [4,1,1,1,1,1,1] => 3 [3,3,3,1] => 1 [3,3,2,2] => 2 [3,3,2,1,1] => 2 [3,3,1,1,1,1] => 3 [3,2,2,2,1] => 1 [3,2,2,1,1,1] => 2 [3,2,1,1,1,1,1] => 2 [3,1,1,1,1,1,1,1] => 3 [2,2,2,2,2] => 2 [2,2,2,2,1,1] => 3 [2,2,2,1,1,1,1] => 3 [2,2,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1] => 4 [1,1,1,1,1,1,1,1,1,1] => 5 [11] => 0 [10,1] => 0 [9,2] => 0 [9,1,1] => 1 [8,3] => 0 [8,2,1] => 0 [8,1,1,1] => 1 [7,4] => 0 [7,2,2] => 1 [7,2,1,1] => 1 [7,1,1,1,1] => 2 [6,5] => 0 [6,4,1] => 0 [6,3,2] => 0 [6,3,1,1] => 1 [6,2,2,1] => 1 [6,2,1,1,1] => 1 [6,1,1,1,1,1] => 2 [5,5,1] => 1 [5,4,2] => 0 [5,4,1,1] => 1 [5,3,3] => 1 [5,3,2,1] => 0 [5,3,1,1,1] => 1 [5,2,2,2] => 1 [5,2,2,1,1] => 2 [5,2,1,1,1,1] => 2 [5,1,1,1,1,1,1] => 3 [4,4,3] => 1 [4,4,2,1] => 1 [4,4,1,1,1] => 2 [4,3,3,1] => 1 [4,3,2,2] => 1 [4,3,2,1,1] => 1 [4,3,1,1,1,1] => 2 [4,2,2,2,1] => 1 [4,2,2,1,1,1] => 2 [4,1,1,1,1,1,1,1] => 3 [3,3,3,2] => 1 [3,3,3,1,1] => 2 [3,3,2,2,1] => 2 [3,3,2,1,1,1] => 2 [3,3,1,1,1,1,1] => 3 [3,2,2,2,2] => 2 [3,2,2,2,1,1] => 2 [3,2,2,1,1,1,1] => 3 [3,2,1,1,1,1,1,1] => 3 [3,1,1,1,1,1,1,1,1] => 4 [2,2,2,2,2,1] => 2 [2,2,2,2,1,1,1] => 3 [2,2,2,1,1,1,1,1] => 3 [2,2,1,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1,1] => 4 [1,1,1,1,1,1,1,1,1,1,1] => 5 [12] => 0 [11,1] => 0 [10,2] => 0 [10,1,1] => 1 [9,3] => 0 [9,2,1] => 0 [9,1,1,1] => 1 [8,4] => 0 [8,3,1] => 0 [8,2,2] => 1 [8,2,1,1] => 1 [8,1,1,1,1] => 2 [7,5] => 0 [7,4,1] => 0 [7,3,2] => 0 [7,3,1,1] => 1 [7,2,2,1] => 1 [7,1,1,1,1,1] => 2 [6,6] => 1 [6,5,1] => 0 [6,4,2] => 0 [6,4,1,1] => 1 [6,3,3] => 1 [6,3,1,1,1] => 1 [6,2,2,2] => 1 [6,2,2,1,1] => 2 [6,2,1,1,1,1] => 2 [6,1,1,1,1,1,1] => 3 [5,5,2] => 1 [5,5,1,1] => 2 [5,4,3] => 0 [5,4,2,1] => 0 [5,4,1,1,1] => 1 [5,3,3,1] => 1 [5,3,2,2] => 1 [5,3,2,1,1] => 1 [5,3,1,1,1,1] => 2 [5,2,2,2,1] => 1 [5,2,2,1,1,1] => 2 [5,2,1,1,1,1,1] => 2 [5,1,1,1,1,1,1,1] => 3 [4,4,4] => 1 [4,4,3,1] => 1 [4,4,2,2] => 2 [4,4,2,1,1] => 2 [4,3,3,2] => 1 [4,3,3,1,1] => 2 [4,3,2,2,1] => 1 [4,3,1,1,1,1,1] => 2 [4,2,2,2,2] => 2 [4,2,2,1,1,1,1] => 3 [4,2,1,1,1,1,1,1] => 3 [4,1,1,1,1,1,1,1,1] => 4 [3,3,3,3] => 2 [3,3,3,2,1] => 1 [3,3,3,1,1,1] => 2 [3,3,2,2,2] => 2 [3,3,2,2,1,1] => 3 [3,3,1,1,1,1,1,1] => 4 [3,2,2,2,2,1] => 2 [3,2,2,1,1,1,1,1] => 3 [3,2,1,1,1,1,1,1,1] => 3 [3,1,1,1,1,1,1,1,1,1] => 4 [2,2,2,2,2,2] => 3 [2,2,2,2,2,1,1] => 3 [2,2,2,2,1,1,1,1] => 4 [2,2,2,1,1,1,1,1,1] => 4 [2,2,1,1,1,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1,1,1,1] => 5 [1,1,1,1,1,1,1,1,1,1,1,1] => 6 [13] => 0 [12,1] => 0 [10,3] => 0 [9,4] => 0 [9,2,2] => 1 [9,2,1,1] => 1 [8,5] => 0 [8,4,1] => 0 [8,3,2] => 0 [8,3,1,1] => 1 [7,6] => 0 [7,5,1] => 0 [7,4,2] => 0 [7,4,1,1] => 1 [7,3,3] => 1 [7,3,2,1] => 0 [7,2,2,2] => 1 [7,2,1,1,1,1] => 2 [7,1,1,1,1,1,1] => 3 [6,6,1] => 1 [6,5,2] => 0 [6,5,1,1] => 1 [6,4,3] => 0 [6,4,2,1] => 0 [6,3,3,1] => 1 [6,3,2,2] => 1 [6,3,1,1,1,1] => 2 [6,2,2,2,1] => 1 [6,2,2,1,1,1] => 2 [6,1,1,1,1,1,1,1] => 3 [5,5,3] => 1 [5,5,2,1] => 1 [5,4,4] => 1 [5,4,3,1] => 0 [5,4,2,2] => 1 [5,4,2,1,1] => 1 [5,4,1,1,1,1] => 2 [5,3,3,2] => 1 [5,3,3,1,1] => 2 [5,3,2,2,1] => 1 [5,3,2,1,1,1] => 1 [5,3,1,1,1,1,1] => 2 [5,2,2,2,1,1] => 2 [5,2,2,1,1,1,1] => 3 [5,2,1,1,1,1,1,1] => 3 [4,4,4,1] => 1 [4,4,3,2] => 1 [4,4,3,1,1] => 2 [4,4,2,2,1] => 2 [4,3,3,3] => 1 [4,3,3,2,1] => 1 [4,2,2,2,2,1] => 2 [3,3,3,3,1] => 2 [3,3,3,2,2] => 2 [3,3,3,2,1,1] => 2 [3,3,2,2,2,1] => 2 [3,3,2,2,1,1,1] => 3 [3,3,2,1,1,1,1,1] => 3 [3,3,1,1,1,1,1,1,1] => 4 [3,2,2,2,2,2] => 2 [3,2,2,2,2,1,1] => 3 [3,2,2,1,1,1,1,1,1] => 4 [3,2,1,1,1,1,1,1,1,1] => 4 [3,1,1,1,1,1,1,1,1,1,1] => 5 [2,2,2,2,2,2,1] => 3 [2,2,2,2,1,1,1,1,1] => 4 [2,2,2,1,1,1,1,1,1,1] => 4 [2,2,1,1,1,1,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1,1,1,1,1] => 5 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 6 [14] => 0 [13,1] => 0 [12,2] => 0 [12,1,1] => 1 [11,2,1] => 0 [11,1,1,1] => 1 [10,2,2] => 1 [9,5] => 0 [9,4,1] => 0 [9,2,2,1] => 1 [8,6] => 0 [8,5,1] => 0 [8,4,2] => 0 [8,3,3] => 1 [8,3,1,1,1] => 1 [8,1,1,1,1,1,1] => 3 [7,7] => 1 [7,6,1] => 0 [7,5,2] => 0 [7,4,3] => 0 [7,2,2,2,1] => 1 [6,6,2] => 1 [6,6,1,1] => 2 [6,5,3] => 0 [6,5,1,1,1] => 1 [6,4,4] => 1 [6,4,2,2] => 1 [6,2,2,2,2] => 2 [6,1,1,1,1,1,1,1,1] => 4 [5,5,4] => 1 [5,5,1,1,1,1] => 3 [5,4,4,1] => 1 [5,4,3,2] => 0 [5,4,3,1,1] => 1 [5,4,2,2,1] => 1 [5,4,2,1,1,1] => 1 [5,4,1,1,1,1,1] => 2 [5,3,3,3] => 1 [5,3,3,2,1] => 1 [5,3,2,2,2] => 1 [5,3,2,2,1,1] => 2 [5,3,2,1,1,1,1] => 2 [5,3,1,1,1,1,1,1] => 3 [5,2,2,2,2,1] => 2 [5,2,2,1,1,1,1,1] => 3 [4,4,4,2] => 1 [4,4,4,1,1] => 2 [4,4,3,3] => 2 [4,4,3,2,1] => 1 [4,3,2,2,2,1] => 1 [3,3,3,3,2] => 2 [3,3,3,3,1,1] => 3 [3,3,3,2,2,1] => 2 [3,3,2,2,2,2] => 3 [3,3,1,1,1,1,1,1,1,1] => 5 [3,2,2,2,2,1,1,1] => 3 [2,2,2,2,2,2,2] => 3 [2,2,2,2,1,1,1,1,1,1] => 5 [2,2,2,1,1,1,1,1,1,1,1] => 5 [2,2,1,1,1,1,1,1,1,1,1,1] => 6 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 6 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 7 [15] => 0 [14,1] => 0 [12,3] => 0 [11,2,2] => 1 [9,6] => 0 [9,5,1] => 0 [9,3,2,1] => 0 [8,7] => 0 [8,5,2] => 0 [7,5,3] => 0 [6,6,3] => 1 [6,5,4] => 0 [6,5,1,1,1,1] => 2 [6,4,3,1,1] => 1 [6,3,3,3] => 1 [6,3,1,1,1,1,1,1] => 3 [6,2,2,2,2,1] => 2 [5,5,5] => 1 [5,5,2,2,1] => 2 [5,4,3,3] => 1 [5,4,3,2,1] => 0 [5,4,3,1,1,1] => 1 [5,3,2,2,2,1] => 1 [5,3,2,2,1,1,1] => 2 [5,3,1,1,1,1,1,1,1] => 3 [4,4,4,3] => 1 [4,4,4,1,1,1] => 2 [4,3,3,3,2] => 1 [3,3,3,3,3] => 2 [3,3,3,3,2,1] => 2 [3,3,3,2,2,2] => 2 [2,2,2,2,2,2,2,1] => 3 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 7 [16] => 0 [15,1] => 0 [12,4] => 0 [12,1,1,1,1] => 2 [10,6] => 0 [9,1,1,1,1,1,1,1] => 3 [8,8] => 1 [8,6,2] => 0 [8,5,3] => 0 [7,6,3] => 0 [7,5,3,1] => 0 [7,5,1,1,1,1] => 2 [7,3,3,2,1] => 1 [6,6,4] => 1 [6,6,2,2] => 2 [6,5,5] => 1 [6,4,3,3] => 1 [5,5,3,3] => 2 [5,5,2,2,2] => 2 [5,4,4,3] => 1 [5,4,3,2,1,1] => 1 [5,4,2,2,2,1] => 1 [4,4,4,4] => 2 [4,4,4,2,2] => 2 [4,4,3,3,2] => 2 [4,4,2,2,2,2] => 3 [4,3,3,3,3] => 2 [4,3,3,3,2,1] => 1 [3,3,3,3,3,1] => 2 [3,3,3,3,2,2] => 3 [3,3,3,3,1,1,1,1] => 4 [3,3,2,2,2,2,2] => 3 [2,2,2,2,2,2,2,2] => 4 [2,2,2,2,2,2,1,1,1,1] => 5 [2,2,2,2,1,1,1,1,1,1,1,1] => 6 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 8 [17] => 0 [16,1] => 0 [9,8] => 0 [8,8,1] => 1 [8,6,3] => 0 [7,6,1,1,1,1] => 2 [7,5,3,2] => 0 [6,5,3,3] => 1 [6,5,2,2,2] => 1 [6,4,4,3] => 1 [6,4,4,1,1,1] => 2 [6,3,3,3,2] => 1 [6,3,3,3,1,1] => 2 [5,5,4,3] => 1 [5,5,4,1,1,1] => 2 [5,5,2,2,2,1] => 2 [5,4,4,4] => 1 [5,4,3,2,2,1] => 1 [5,3,3,3,2,1] => 1 [4,4,4,3,2] => 1 [4,4,4,3,1,1] => 2 [4,4,4,2,2,1] => 2 [4,4,3,3,3] => 2 [3,3,3,3,3,2] => 2 [3,2,2,2,2,2,2,2] => 3 [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 7 [4,4,4,3,2,1] => 1 [5,4,3,3,2,1] => 1 [6,3,3,3,2,1] => 1 [6,5,2,2,2,1] => 1 [5,5,3,3,1,1] => 3 [6,5,4,1,1,1] => 1 [5,5,3,3,2] => 2 [5,5,4,2,2] => 2 [6,4,4,2,2] => 2 [6,5,4,3] => 0 [3,3,3,3,3,2,1] => 2 [4,4,4,3,3] => 2 [4,4,4,4,2] => 2 [5,5,4,4] => 2 [6,4,4,4] => 1 [7,6,5] => 0 [2,2,2,2,2,2,2,2,2] => 4 [3,3,3,3,3,3] => 3 [18] => 0 [6,2,2,2,2,2,2] => 3 [6,6,6] => 1 [4,2,2,2,2,2,2,2] => 3 [10,4,4] => 1 [9,6,3] => 0 [8,6,4] => 0 [10,8] => 0 [3,3,3,3,1,1,1,1,1,1] => 5 [9,9] => 1 [7,7,1,1,1,1] => 3 [9,1,1,1,1,1,1,1,1,1] => 4 [7,7,4] => 1 [5,4,4,3,2,1] => 1 [5,5,3,3,2,1] => 2 [5,5,4,2,2,1] => 2 [6,4,4,2,2,1] => 2 [5,5,4,3,1,1] => 2 [6,4,4,3,1,1] => 2 [6,5,3,3,1,1] => 2 [5,5,4,3,2] => 1 [6,4,4,3,2] => 1 [6,5,3,3,2] => 1 [6,5,4,2,2] => 1 [6,5,4,3,1] => 0 [6,5,4,1,1,1,1] => 2 [4,4,4,4,3] => 2 [4,3,3,3,3,3] => 2 [19] => 0 [7,2,2,2,2,2,2] => 3 [7,6,6] => 1 [5,2,2,2,2,2,2,2] => 3 [13,6] => 0 [11,4,4] => 1 [9,6,4] => 0 [8,5,4,2] => 0 [8,5,5,1] => 1 [5,5,4,3,2,1] => 1 [6,4,4,3,2,1] => 1 [6,5,3,3,2,1] => 1 [6,5,4,2,2,1] => 1 [6,5,4,3,1,1] => 1 [6,5,4,3,2] => 0 [6,5,2,2,2,2,1] => 2 [6,5,4,2,1,1,1] => 1 [6,6,2,2,2,2] => 3 [7,5,4,3,1] => 0 [2,2,2,2,2,2,2,2,2,2] => 5 [3,3,3,3,3,3,2] => 3 [4,4,3,3,3,3] => 3 [4,4,4,4,4] => 2 [5,5,5,5] => 2 [20] => 0 [10,10] => 1 [8,2,2,2,2,2,2] => 3 [8,6,4,2] => 0 [8,6,6] => 1 [10,6,4] => 0 [9,8,3] => 0 [6,6,6,2] => 1 [10,7,3] => 0 [9,7,4] => 0 [9,5,5,1] => 1 [12,5,1,1,1] => 1 [11,1,1,1,1,1,1,1,1,1] => 4 [6,5,4,3,2,1] => 0 [6,3,3,3,3,2,1] => 2 [6,5,3,2,2,2,1] => 1 [6,5,4,3,1,1,1] => 1 [7,6,2,2,2,2] => 2 [6,6,5,4] => 1 [3,3,3,3,3,3,3] => 3 [4,4,4,3,3,3] => 2 [21] => 0 [11,7,3] => 0 [5,4,2,2,2,2,2,2] => 3 [11,10] => 0 [13,4,4] => 1 [7,6,6,2] => 1 [4,4,4,4,3,2,1] => 2 [6,4,3,3,3,2,1] => 1 [6,5,4,2,2,2,1] => 1 [6,5,4,3,2,1,1] => 1 [4,4,4,4,3,3] => 3 [8,6,2,2,2,2] => 2 [22] => 0 [9,6,4,3] => 0 [8,7,7] => 1 [5,4,4,4,3,2,1] => 1 [6,5,3,3,3,2,1] => 1 [6,5,4,3,2,2,1] => 1 [15,2,2,2,2] => 2 [9,6,5,3] => 0 [8,6,5,3,1] => 0 [6,4,4,4,3,2,1] => 1 [6,5,4,3,3,2,1] => 1 [3,3,3,3,3,3,3,3] => 4 [4,4,4,4,4,4] => 3 [6,6,6,6] => 2 [24] => 0 [11,7,5,1] => 0 [9,7,5,3] => 0 [8,8,8] => 1 [3,3,3,3,3,3,3,2,1] => 3 [17,7] => 0 [12,9,3] => 0 [9,8,1,1,1,1,1,1,1] => 3 [13,1,1,1,1,1,1,1,1,1,1,1] => 5 [5,5,5,4,3,2,1] => 1 [6,5,4,4,3,2,1] => 1 [7,6,6,6] => 1 [5,4,4,4,2,2,2,2] => 3 [13,12] => 0 [15,5,5] => 1 [9,7,5,3,1] => 0 [10,7,5,3] => 0 [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] => 7 [5,5,5,5,5] => 2 [12,10,3] => 0 [11,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 7 [6,5,5,4,3,2,1] => 1 [6,6,4,3,3,2,2] => 3 [8,6,6,6] => 1 [9,7,5,4,1] => 0 [16,8,2] => 0 [6,6,5,4,3,2,1] => 1 [7,6,5,4,3,2] => 0 [3,3,3,3,3,3,3,3,3] => 4 [15,6,6] => 1 [7,6,5,4,3,2,1] => 0 [6,6,6,4,3,3] => 2 [4,3,3,3,3,3,3,3,3] => 4 [7,6,5,4,3,1,1,1] => 1 [10,7,6,4,1] => 0 [9,7,6,4,2] => 0 [10,8,5,4,1] => 0 [15,14] => 0 [7,6,5,4,3,2,1,1] => 1 [7,6,5,4,2,2,2,1] => 1 [10,8,6,4,1] => 0 [6,6,6,6,6] => 2 [30] => 0 [15,15] => 1 [5,5,5,5,5,5] => 3 [6,6,6,6,3,3] => 3 [10,10,10] => 1 [9,7,5,5,3,1] => 1 [7,6,5,4,3,2,2,1] => 1 [7,6,5,3,3,3,2,1] => 1 [11,8,6,4,1] => 0 [10,8,6,4,2] => 0 [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 7 [3,3,3,3,3,3,3,3,3,2,1] => 4 [7,6,6,6,6] => 2 [7,6,5,4,3,3,2,1] => 1 [7,6,4,4,4,3,2,1] => 1 [11,8,6,5,1] => 0 [10,10,9,2] => 1 [14,9,8] => 0 [4,4,4,4,4,4,4,4] => 4 [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 8 [7,6,5,4,4,3,2,1] => 1 [7,5,5,5,4,3,2,1] => 1 [16,16] => 1 [10,10,10,2] => 1 [16,8,4,2,2] => 1 [9,4,4,4,4,4,2,1] => 2 [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 7 [5,4,4,4,4,4,4,4] => 3 [7,6,5,5,4,3,2,1] => 1 [6,6,6,5,4,3,2,1] => 1 [22,7,4] => 0 [12,12,4,3,2] => 1 [4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 7 [7,6,6,5,4,3,2,1] => 1 [12,9,7,5,1] => 0 [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 7 [7,7,6,5,4,3,2,1] => 1 [13,9,7,5,1] => 0 [18,18] => 1 [24,12] => 0 [11,9,7,5,3,1] => 0 [11,8,7,5,4,1] => 0 [8,7,6,5,4,3,2,1] => 0 [8,7,7,7,7] => 2 [7,6,2,2,2,2,2,2,2,2,2,2,2,2] => 6 [7,6,6,6,6,6] => 2 [8,7,6,5,4,3,2,1,1] => 1 [8,7,6,5,4,3,2,2,1] => 1 [8,7,6,5,4,3,3,2,1] => 1 [10,10,10,10] => 2 [12,12,12,4] => 1 [8,7,6,5,4,4,3,2,1] => 1 [11,9,7,5,5,3] => 1 [4,4,4,4,4,4,4,4,4,4] => 5 [14,14,8,4] => 1 [21,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 9 [7,6,6,6,2,2,2,2,2,2,2,2] => 5 [8,7,6,5,5,4,3,2,1] => 1 [9,9,9,9,3,3] => 3 [8,7,6,6,5,4,3,2,1] => 1 [10,10,10,5,5,2] => 2 [16,10,8,8] => 1 [26,9,7] => 0 [8,7,7,6,5,4,3,2,1] => 1 [8,8,7,6,5,4,3,2,1] => 1 [18,18,9] => 1 [9,8,7,6,5,4,3,2,1] => 0 [11,9,7,7,5,3,3] => 2 [48] => 0 [7,6,6,6,6,6,6,6] => 3 [22,9,8,5,5] => 1 [6,6,6,6,6,6,6,3,3,2] => 4 [27,14,9] => 0 [17,14,13,8] => 0 [5,5,5,5,5,5,5,5,5,5,5] => 5 [27,20,8] => 0 [26,13,7,7,2] => 1 [31,12,10,4] => 0 [6,6,6,6,6,6,6,6,6,6] => 5 [5,5,5,5,5,5,5,5,5,5,5,5] => 6 [12,12,12,12,12] => 2 [17,16,2,2,2,2,2,2,2,2,2,2,2,2,2,1] => 6 [12,12,12,12,11,4] => 2 [12,12,12,12,12,4] => 2 [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 15 [11,11,11,11,11,10] => 2 [11,11,11,11,11,11] => 3 [16,14,9,9,9,9] => 2 [8,8,8,8,8,8,8,8,4,2] => 4 [24,24,24] => 1 [16,16,16,16,8,4,2] => 2 [12,12,12,12,12,12,4,4] => 4 [22,20,20,12,8] => 1 [20,20,8,4,4,4,4,4,4,4,4,4] => 5 [33,32,9,9,5] => 1 [18,18,18,18,18] => 2 [18,18,18,18,9,9] => 3 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3] => 8 [56,17,11,10,5] => 0 [33,26,23,12,9] => 0 [22,22,22,10,10,9,4,4] => 3 [22,22,22,10,10,10,4,4] => 3 [12,12,12,12,12,12,12,12,4,3,2] => 4 [24,24,24,24,14] => 2 [76,22,9,6] => 0 [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 11 [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 12 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 10 [12,12,12,12,12,12,12,12,12,12] => 5 [24,24,24,24,24] => 2 [23,22,21,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,1] => 8 [12,12,12,12,12,12,12,12,12,6,6,6,4,2] => 5 [54,48,18,10,8] => 0 [24,24,24,24,24,24] => 3 [37,33,20,20,13,10,10,10,7] => 2 [42,34,30,22,22,14,2] => 1 [54,52,34,18,11,7] => 0 [65,27,27,25,13,9,6,6] => 2 [18,18,18,18,18,18,18,18,18,18] => 5 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 15 [16,16,16,16,16,16,16,8,8,8,8,8,8,8,8,4,2] => 7 [58,38,38,38,30] => 1 [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 10 [10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,2] => 12 [74,58,34,34,22,22,13,11,2] => 2 [61,48,48,48,45,22,12,2] => 1 [15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3] => 11 [98,62,36,26,14,14,14,14,14,14,12,2] => 3 [14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,13,2] => 12 [14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,2] => 12 [74,74,26,26,26,26,12,12,12,12,12,12,6,6,4,4,3,3,3,3] => 10 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 30 [64,57,40,39,28,23,19,19,16,9,8,8,8,8,8,8,6,6] => 5 [70,70,46,28,22,22,10,9,9,9,9,8,8,8,8,8,7,7,7,3,3,3] => 8 [14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,7,7,7,7,7,2] => 16 [170,92,36,28,27,24,20,14,13,10,8,8] => 1 [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,6,6,6,6,4,4,4,3,3] => 21 [145,83,62,44,44,42,19,16,16,10,8] => 2 [98,98,37,37,37,37,24,24,24,24,24,24,24,24,10,10,8,8] => 9 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 60 [11,9,7,6,5,3,1] => 0 [13,11,9,7,5,3,1] => 0 [13,11,9,7,7,5,3,1] => 1 [17,13,11,9,7,5,1] => 0 [15,13,11,9,7,5,3,1] => 0 [29,23,19,17,13,11,7,1] => 0 ----------------------------------------------------------------------------- Created: Jul 08, 2013 at 13:35 by Christian Stump ----------------------------------------------------------------------------- Last Updated: May 02, 2024 at 23:11 by Martin Rubey