***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew <info@findstat.org> * * * * 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: St000137 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The Grundy value of an integer partition. Consider the two-player game on an integer partition. In each move, a player removes either a box, or a 2x2-configuration of boxes such that the resulting diagram is still a partition. The first player that cannot move lose. This happens exactly when the empty partition is reached. The grundy value of an integer partition is defined as the grundy value of this two-player game as defined in [1]. This game was described to me during Norcom 2013, by Urban Larsson, and it seems to be quite difficult to give a good description of the partitions with Grundy value 0. ----------------------------------------------------------------------------- References: [1] [[wikipedia:Sprague–Grundy_theorem]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 0 [1,1] => 0 [3] => 1 [2,1] => 1 [1,1,1] => 1 [4] => 0 [3,1] => 0 [2,2] => 2 [2,1,1] => 0 [1,1,1,1] => 0 [5] => 1 [4,1] => 1 [3,2] => 1 [3,1,1] => 1 [2,2,1] => 1 [2,1,1,1] => 1 [1,1,1,1,1] => 1 [6] => 0 [5,1] => 0 [4,2] => 0 [4,1,1] => 0 [3,3] => 2 [3,2,1] => 0 [3,1,1,1] => 0 [2,2,2] => 2 [2,2,1,1] => 0 [2,1,1,1,1] => 0 [1,1,1,1,1,1] => 0 [7] => 1 [6,1] => 1 [5,2] => 1 [5,1,1] => 1 [4,3] => 1 [4,2,1] => 1 [4,1,1,1] => 1 [3,3,1] => 3 [3,2,2] => 3 [3,2,1,1] => 1 [3,1,1,1,1] => 1 [2,2,2,1] => 1 [2,2,1,1,1] => 1 [2,1,1,1,1,1] => 1 [1,1,1,1,1,1,1] => 1 [8] => 0 [7,1] => 0 [6,2] => 0 [6,1,1] => 0 [5,3] => 0 [5,2,1] => 0 [5,1,1,1] => 0 [4,4] => 0 [4,3,1] => 0 [4,2,2] => 2 [4,2,1,1] => 0 [4,1,1,1,1] => 0 [3,3,2] => 0 [3,3,1,1] => 2 [3,2,2,1] => 0 [3,2,1,1,1] => 0 [3,1,1,1,1,1] => 0 [2,2,2,2] => 0 [2,2,2,1,1] => 0 [2,2,1,1,1,1] => 0 [2,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1] => 0 [9] => 1 [8,1] => 1 [7,2] => 1 [7,1,1] => 1 [6,3] => 1 [6,2,1] => 1 [6,1,1,1] => 1 [5,4] => 1 [5,3,1] => 1 [5,2,2] => 3 [5,2,1,1] => 1 [5,1,1,1,1] => 1 [4,4,1] => 2 [4,3,2] => 1 [4,3,1,1] => 1 [4,2,2,1] => 1 [4,2,1,1,1] => 1 [4,1,1,1,1,1] => 1 [3,3,3] => 2 [3,3,2,1] => 1 [3,3,1,1,1] => 3 [3,2,2,2] => 2 [3,2,2,1,1] => 1 [3,2,1,1,1,1] => 1 [3,1,1,1,1,1,1] => 1 [2,2,2,2,1] => 1 [2,2,2,1,1,1] => 1 [2,2,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1] => 1 [10] => 0 [9,1] => 0 [8,2] => 0 [8,1,1] => 0 [7,3] => 0 [7,2,1] => 0 [7,1,1,1] => 0 [6,4] => 0 [6,3,1] => 0 [6,2,2] => 2 [6,2,1,1] => 0 [6,1,1,1,1] => 0 [5,5] => 0 [5,4,1] => 0 [5,3,2] => 0 [5,3,1,1] => 0 [5,2,2,1] => 0 [5,2,1,1,1] => 0 [5,1,1,1,1,1] => 0 [4,4,2] => 0 [4,4,1,1] => 3 [4,3,3] => 3 [4,3,2,1] => 0 [4,3,1,1,1] => 0 [4,2,2,2] => 3 [4,2,2,1,1] => 0 [4,2,1,1,1,1] => 0 [4,1,1,1,1,1,1] => 0 [3,3,3,1] => 3 [3,3,2,2] => 0 [3,3,2,1,1] => 0 [3,3,1,1,1,1] => 2 [3,2,2,2,1] => 0 [3,2,2,1,1,1] => 0 [3,2,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1] => 0 [2,2,2,2,2] => 0 [2,2,2,2,1,1] => 0 [2,2,2,1,1,1,1] => 0 [2,2,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1] => 0 [11] => 1 [10,1] => 1 [9,2] => 1 [9,1,1] => 1 [8,3] => 1 [8,2,1] => 1 [8,1,1,1] => 1 [7,4] => 1 [7,3,1] => 1 [7,2,2] => 3 [7,2,1,1] => 1 [7,1,1,1,1] => 1 [6,5] => 1 [6,4,1] => 1 [6,3,2] => 1 [6,3,1,1] => 1 [6,2,2,1] => 1 [6,2,1,1,1] => 1 [6,1,1,1,1,1] => 1 [5,5,1] => 1 [5,4,2] => 1 [5,4,1,1] => 1 [5,3,3] => 2 [5,3,2,1] => 1 [5,3,1,1,1] => 1 [5,2,2,2] => 2 [5,2,2,1,1] => 1 [5,2,1,1,1,1] => 1 [5,1,1,1,1,1,1] => 1 [4,4,3] => 1 [4,4,2,1] => 2 [4,4,1,1,1] => 2 [4,3,3,1] => 2 [4,3,2,2] => 2 [4,3,2,1,1] => 1 [4,3,1,1,1,1] => 1 [4,2,2,2,1] => 1 [4,2,2,1,1,1] => 1 [4,2,1,1,1,1,1] => 1 [4,1,1,1,1,1,1,1] => 1 [3,3,3,2] => 1 [3,3,3,1,1] => 2 [3,3,2,2,1] => 1 [3,3,2,1,1,1] => 1 [3,3,1,1,1,1,1] => 3 [3,2,2,2,2] => 1 [3,2,2,2,1,1] => 1 [3,2,2,1,1,1,1] => 1 [3,2,1,1,1,1,1,1] => 1 [3,1,1,1,1,1,1,1,1] => 1 [2,2,2,2,2,1] => 1 [2,2,2,2,1,1,1] => 1 [2,2,2,1,1,1,1,1] => 1 [2,2,1,1,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1,1] => 1 [12] => 0 [11,1] => 0 [10,2] => 0 [10,1,1] => 0 [9,3] => 0 [9,2,1] => 0 [9,1,1,1] => 0 [8,4] => 0 [8,3,1] => 0 [8,2,2] => 2 [8,2,1,1] => 0 [8,1,1,1,1] => 0 [7,5] => 0 [7,4,1] => 0 [7,3,2] => 0 [7,3,1,1] => 0 [7,2,2,1] => 0 [7,2,1,1,1] => 0 [7,1,1,1,1,1] => 0 [6,6] => 2 [6,5,1] => 0 [6,4,2] => 0 [6,4,1,1] => 0 [6,3,3] => 3 [6,3,2,1] => 0 [6,3,1,1,1] => 0 [6,2,2,2] => 3 [6,2,2,1,1] => 0 [6,2,1,1,1,1] => 0 [6,1,1,1,1,1,1] => 0 [5,5,2] => 2 [5,5,1,1] => 0 [5,4,3] => 0 [5,4,2,1] => 0 [5,4,1,1,1] => 0 [5,3,3,1] => 3 [5,3,2,2] => 3 [5,3,2,1,1] => 0 [5,3,1,1,1,1] => 0 [5,2,2,2,1] => 0 [5,2,2,1,1,1] => 0 [5,2,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1] => 0 [4,4,4] => 0 [4,4,3,1] => 0 [4,4,2,2] => 1 [4,4,2,1,1] => 3 [4,4,1,1,1,1] => 3 [4,3,3,2] => 0 [4,3,3,1,1] => 3 [4,3,2,2,1] => 0 [4,3,2,1,1,1] => 0 [4,3,1,1,1,1,1] => 0 [4,2,2,2,2] => 0 [4,2,2,2,1,1] => 0 [4,2,2,1,1,1,1] => 0 [4,2,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1] => 0 [3,3,3,3] => 0 [3,3,3,2,1] => 0 [3,3,3,1,1,1] => 3 [3,3,2,2,2] => 2 [3,3,2,2,1,1] => 0 [3,3,2,1,1,1,1] => 0 [3,3,1,1,1,1,1,1] => 2 [3,2,2,2,2,1] => 0 [3,2,2,2,1,1,1] => 0 [3,2,2,1,1,1,1,1] => 0 [3,2,1,1,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2] => 2 [2,2,2,2,2,1,1] => 0 [2,2,2,2,1,1,1,1] => 0 [2,2,2,1,1,1,1,1,1] => 0 [2,2,1,1,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1,1,1] => 0 [13] => 1 [12,1] => 1 [11,2] => 1 [11,1,1] => 1 [10,3] => 1 [10,2,1] => 1 [10,1,1,1] => 1 [9,4] => 1 [9,3,1] => 1 [9,2,2] => 3 [9,2,1,1] => 1 [9,1,1,1,1] => 1 [8,5] => 1 [8,4,1] => 1 [8,3,2] => 1 [8,3,1,1] => 1 [8,2,2,1] => 1 [8,2,1,1,1] => 1 [8,1,1,1,1,1] => 1 [7,6] => 1 [7,5,1] => 1 [7,4,2] => 1 [7,4,1,1] => 1 [7,3,3] => 2 [7,3,2,1] => 1 [7,3,1,1,1] => 1 [7,2,2,2] => 2 [7,2,2,1,1] => 1 [7,2,1,1,1,1] => 1 [7,1,1,1,1,1,1] => 1 [6,6,1] => 1 [6,5,2] => 1 [6,5,1,1] => 1 [6,4,3] => 1 [6,4,2,1] => 1 [6,4,1,1,1] => 1 [6,3,3,1] => 2 [6,3,2,2] => 2 [6,3,2,1,1] => 1 [6,3,1,1,1,1] => 1 [6,2,2,2,1] => 1 [6,2,2,1,1,1] => 1 [6,2,1,1,1,1,1] => 1 [6,1,1,1,1,1,1,1] => 1 [5,5,3] => 1 [5,5,2,1] => 3 [5,5,1,1,1] => 1 [5,4,4] => 1 [5,4,3,1] => 1 [5,4,2,2] => 2 [5,4,2,1,1] => 1 [5,4,1,1,1,1] => 1 [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] => 1 [5,2,2,2,2] => 1 [5,2,2,2,1,1] => 1 [5,2,2,1,1,1,1] => 1 [5,2,1,1,1,1,1,1] => 1 [5,1,1,1,1,1,1,1,1] => 1 [4,4,4,1] => 2 [4,4,3,2] => 2 [4,4,3,1,1] => 1 [4,4,2,2,1] => 2 [4,4,2,1,1,1] => 2 [4,4,1,1,1,1,1] => 2 [4,3,3,3] => 2 [4,3,3,2,1] => 1 [4,3,3,1,1,1] => 2 [4,3,2,2,2] => 3 [4,3,2,2,1,1] => 1 [4,3,2,1,1,1,1] => 1 [4,3,1,1,1,1,1,1] => 1 [4,2,2,2,2,1] => 1 [4,2,2,2,1,1,1] => 1 [4,2,2,1,1,1,1,1] => 1 [4,2,1,1,1,1,1,1,1] => 1 [4,1,1,1,1,1,1,1,1,1] => 1 [3,3,3,3,1] => 1 [3,3,3,2,2] => 1 [3,3,3,2,1,1] => 1 [3,3,3,1,1,1,1] => 2 [3,3,2,2,2,1] => 1 [3,3,2,2,1,1,1] => 1 [3,3,2,1,1,1,1,1] => 1 [3,3,1,1,1,1,1,1,1] => 3 [3,2,2,2,2,2] => 1 [3,2,2,2,2,1,1] => 1 [3,2,2,2,1,1,1,1] => 1 [3,2,2,1,1,1,1,1,1] => 1 [3,2,1,1,1,1,1,1,1,1] => 1 [3,1,1,1,1,1,1,1,1,1,1] => 1 [2,2,2,2,2,2,1] => 1 [2,2,2,2,2,1,1,1] => 1 [2,2,2,2,1,1,1,1,1] => 1 [2,2,2,1,1,1,1,1,1,1] => 1 [2,2,1,1,1,1,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [14] => 0 [13,1] => 0 [12,2] => 0 [12,1,1] => 0 [11,3] => 0 [11,2,1] => 0 [11,1,1,1] => 0 [10,4] => 0 [10,3,1] => 0 [10,2,2] => 2 [10,2,1,1] => 0 [10,1,1,1,1] => 0 [9,5] => 0 [9,4,1] => 0 [9,3,2] => 0 [9,3,1,1] => 0 [9,2,2,1] => 0 [9,2,1,1,1] => 0 [9,1,1,1,1,1] => 0 [8,6] => 0 [8,5,1] => 0 [8,4,2] => 0 [8,4,1,1] => 0 [8,3,3] => 3 [8,3,2,1] => 0 [8,3,1,1,1] => 0 [8,2,2,2] => 3 [8,2,2,1,1] => 0 [8,2,1,1,1,1] => 0 [8,1,1,1,1,1,1] => 0 [7,7] => 2 [7,6,1] => 0 [7,5,2] => 0 [7,5,1,1] => 0 [7,4,3] => 0 [7,4,2,1] => 0 [7,4,1,1,1] => 0 [7,3,3,1] => 3 [7,3,2,2] => 3 [7,3,2,1,1] => 0 [7,3,1,1,1,1] => 0 [7,2,2,2,1] => 0 [7,2,2,1,1,1] => 0 [7,2,1,1,1,1,1] => 0 [7,1,1,1,1,1,1,1] => 0 [6,6,2] => 2 [6,6,1,1] => 0 [6,5,3] => 0 [6,5,2,1] => 0 [6,5,1,1,1] => 0 [6,4,4] => 0 [6,4,3,1] => 0 [6,4,2,2] => 3 [6,4,2,1,1] => 0 [6,4,1,1,1,1] => 0 [6,3,3,2] => 0 [6,3,3,1,1] => 3 [6,3,2,2,1] => 0 [6,3,2,1,1,1] => 0 [6,3,1,1,1,1,1] => 0 [6,2,2,2,2] => 0 [6,2,2,2,1,1] => 0 [6,2,2,1,1,1,1] => 0 [6,2,1,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1,1] => 0 [5,5,4] => 0 [5,5,3,1] => 0 [5,5,2,2] => 1 [5,5,2,1,1] => 2 [5,5,1,1,1,1] => 0 [5,4,4,1] => 3 [5,4,3,2] => 0 [5,4,3,1,1] => 0 [5,4,2,2,1] => 0 [5,4,2,1,1,1] => 0 [5,4,1,1,1,1,1] => 0 [5,3,3,3] => 3 [5,3,3,2,1] => 0 [5,3,3,1,1,1] => 3 [5,3,2,2,2] => 2 [5,3,2,2,1,1] => 0 [5,3,2,1,1,1,1] => 0 [5,3,1,1,1,1,1,1] => 0 [5,2,2,2,2,1] => 0 [5,2,2,2,1,1,1] => 0 [5,2,2,1,1,1,1,1] => 0 [5,2,1,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1,1] => 0 [4,4,4,2] => 0 [4,4,4,1,1] => 3 [4,4,3,3] => 0 [4,4,3,2,1] => 0 [4,4,3,1,1,1] => 0 [4,4,2,2,2] => 1 [4,4,2,2,1,1] => 3 [4,4,2,1,1,1,1] => 3 [4,4,1,1,1,1,1,1] => 3 [4,3,3,3,1] => 3 [4,3,3,2,2] => 0 [4,3,3,2,1,1] => 0 [4,3,3,1,1,1,1] => 3 [4,3,2,2,2,1] => 0 [4,3,2,2,1,1,1] => 0 [4,3,2,1,1,1,1,1] => 0 [4,3,1,1,1,1,1,1,1] => 0 [4,2,2,2,2,2] => 0 [4,2,2,2,2,1,1] => 0 [4,2,2,2,1,1,1,1] => 0 [4,2,2,1,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,2] => 0 [3,3,3,3,1,1] => 0 [3,3,3,2,2,1] => 0 [3,3,3,2,1,1,1] => 0 [3,3,3,1,1,1,1,1] => 3 [3,3,2,2,2,2] => 2 [3,3,2,2,2,1,1] => 0 [3,3,2,2,1,1,1,1] => 0 [3,3,2,1,1,1,1,1,1] => 0 [3,3,1,1,1,1,1,1,1,1] => 2 [3,2,2,2,2,2,1] => 0 [3,2,2,2,2,1,1,1] => 0 [3,2,2,2,1,1,1,1,1] => 0 [3,2,2,1,1,1,1,1,1,1] => 0 [3,2,1,1,1,1,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2,2] => 2 [2,2,2,2,2,2,1,1] => 0 [2,2,2,2,2,1,1,1,1] => 0 [2,2,2,2,1,1,1,1,1,1] => 0 [2,2,2,1,1,1,1,1,1,1,1] => 0 [2,2,1,1,1,1,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [15] => 1 [14,1] => 1 [13,2] => 1 [13,1,1] => 1 [12,3] => 1 [12,2,1] => 1 [12,1,1,1] => 1 [11,4] => 1 [11,3,1] => 1 [11,2,2] => 3 [11,2,1,1] => 1 [11,1,1,1,1] => 1 [10,5] => 1 [10,4,1] => 1 [10,3,2] => 1 [10,3,1,1] => 1 [10,2,2,1] => 1 [10,2,1,1,1] => 1 [10,1,1,1,1,1] => 1 [9,6] => 1 [9,5,1] => 1 [9,4,2] => 1 [9,4,1,1] => 1 [9,3,3] => 2 [9,3,2,1] => 1 [9,3,1,1,1] => 1 [9,2,2,2] => 2 [9,2,2,1,1] => 1 [9,2,1,1,1,1] => 1 [9,1,1,1,1,1,1] => 1 [8,7] => 1 [8,6,1] => 1 [8,5,2] => 1 [8,5,1,1] => 1 [8,4,3] => 1 [8,4,2,1] => 1 [8,4,1,1,1] => 1 [8,3,3,1] => 2 [8,3,2,2] => 2 [8,3,2,1,1] => 1 [8,3,1,1,1,1] => 1 [8,2,2,2,1] => 1 [8,2,2,1,1,1] => 1 [8,2,1,1,1,1,1] => 1 [8,1,1,1,1,1,1,1] => 1 [7,7,1] => 3 [7,6,2] => 1 [7,6,1,1] => 1 [7,5,3] => 1 [7,5,2,1] => 1 [7,5,1,1,1] => 1 [7,4,4] => 1 [7,4,3,1] => 1 [7,4,2,2] => 2 [7,4,2,1,1] => 1 [7,4,1,1,1,1] => 1 [7,3,3,2] => 1 [7,3,3,1,1] => 2 [7,3,2,2,1] => 1 [7,3,2,1,1,1] => 1 [7,3,1,1,1,1,1] => 1 [7,2,2,2,2] => 1 [7,2,2,2,1,1] => 1 [7,2,2,1,1,1,1] => 1 [7,2,1,1,1,1,1,1] => 1 [7,1,1,1,1,1,1,1,1] => 1 [6,6,3] => 3 [6,6,2,1] => 1 [6,6,1,1,1] => 1 [6,5,4] => 1 [6,5,3,1] => 1 [6,5,2,2] => 2 [6,5,2,1,1] => 1 [6,5,1,1,1,1] => 1 [6,4,4,1] => 2 [6,4,3,2] => 1 [6,4,3,1,1] => 1 [6,4,2,2,1] => 1 [6,4,2,1,1,1] => 1 [6,4,1,1,1,1,1] => 1 [6,3,3,3] => 2 [6,3,3,2,1] => 1 [6,3,3,1,1,1] => 2 [6,3,2,2,2] => 3 [6,3,2,2,1,1] => 1 [6,3,2,1,1,1,1] => 1 [6,3,1,1,1,1,1,1] => 1 [6,2,2,2,2,1] => 1 [6,2,2,2,1,1,1] => 1 [6,2,2,1,1,1,1,1] => 1 [6,2,1,1,1,1,1,1,1] => 1 [6,1,1,1,1,1,1,1,1,1] => 1 [5,5,5] => 1 [5,5,4,1] => 1 [5,5,3,2] => 2 [5,5,3,1,1] => 1 [5,5,2,2,1] => 3 [5,5,2,1,1,1] => 3 [5,5,1,1,1,1,1] => 1 [5,4,4,2] => 1 [5,4,4,1,1] => 2 [5,4,3,3] => 2 [5,4,3,2,1] => 1 [5,4,3,1,1,1] => 1 [5,4,2,2,2] => 3 [5,4,2,2,1,1] => 1 [5,4,2,1,1,1,1] => 1 [5,4,1,1,1,1,1,1] => 1 [5,3,3,3,1] => 2 [5,3,3,2,2] => 1 [5,3,3,2,1,1] => 1 [5,3,3,1,1,1,1] => 2 [5,3,2,2,2,1] => 1 [5,3,2,2,1,1,1] => 1 [5,3,2,1,1,1,1,1] => 1 [5,3,1,1,1,1,1,1,1] => 1 [5,2,2,2,2,2] => 1 [5,2,2,2,2,1,1] => 1 [5,2,2,2,1,1,1,1] => 1 [5,2,2,1,1,1,1,1,1] => 1 [5,2,1,1,1,1,1,1,1,1] => 1 [5,1,1,1,1,1,1,1,1,1,1] => 1 [4,4,4,3] => 1 [4,4,4,2,1] => 2 [4,4,4,1,1,1] => 2 [4,4,3,3,1] => 1 [4,4,3,2,2] => 2 [4,4,3,2,1,1] => 1 [4,4,3,1,1,1,1] => 1 [4,4,2,2,2,1] => 2 [4,4,2,2,1,1,1] => 2 [4,4,2,1,1,1,1,1] => 2 [4,4,1,1,1,1,1,1,1] => 2 [4,3,3,3,2] => 1 [4,3,3,3,1,1] => 2 [4,3,3,2,2,1] => 1 [4,3,3,2,1,1,1] => 1 [4,3,3,1,1,1,1,1] => 2 [4,3,2,2,2,2] => 1 [4,3,2,2,2,1,1] => 1 [4,3,2,2,1,1,1,1] => 1 [4,3,2,1,1,1,1,1,1] => 1 [4,3,1,1,1,1,1,1,1,1] => 1 [4,2,2,2,2,2,1] => 1 [4,2,2,2,2,1,1,1] => 1 [4,2,2,2,1,1,1,1,1] => 1 [4,2,2,1,1,1,1,1,1,1] => 1 [4,2,1,1,1,1,1,1,1,1,1] => 1 [4,1,1,1,1,1,1,1,1,1,1,1] => 1 [3,3,3,3,3] => 1 [3,3,3,3,2,1] => 1 [3,3,3,3,1,1,1] => 1 [3,3,3,2,2,2] => 3 [3,3,3,2,2,1,1] => 1 [3,3,3,2,1,1,1,1] => 1 [3,3,3,1,1,1,1,1,1] => 2 [3,3,2,2,2,2,1] => 1 [3,3,2,2,2,1,1,1] => 1 [3,3,2,2,1,1,1,1,1] => 1 [3,3,2,1,1,1,1,1,1,1] => 1 [3,3,1,1,1,1,1,1,1,1,1] => 3 [3,2,2,2,2,2,2] => 3 [3,2,2,2,2,2,1,1] => 1 [3,2,2,2,2,1,1,1,1] => 1 [3,2,2,2,1,1,1,1,1,1] => 1 [3,2,2,1,1,1,1,1,1,1,1] => 1 [3,2,1,1,1,1,1,1,1,1,1,1] => 1 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [2,2,2,2,2,2,2,1] => 1 [2,2,2,2,2,2,1,1,1] => 1 [2,2,2,2,2,1,1,1,1,1] => 1 [2,2,2,2,1,1,1,1,1,1,1] => 1 [2,2,2,1,1,1,1,1,1,1,1,1] => 1 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [16] => 0 [15,1] => 0 [14,2] => 0 [14,1,1] => 0 [13,3] => 0 [13,2,1] => 0 [13,1,1,1] => 0 [12,4] => 0 [12,3,1] => 0 [12,2,2] => 2 [12,2,1,1] => 0 [12,1,1,1,1] => 0 [11,5] => 0 [11,4,1] => 0 [11,3,2] => 0 [11,3,1,1] => 0 [11,2,2,1] => 0 [11,2,1,1,1] => 0 [11,1,1,1,1,1] => 0 [10,6] => 0 [10,5,1] => 0 [10,4,2] => 0 [10,4,1,1] => 0 [10,3,3] => 3 [10,3,2,1] => 0 [10,3,1,1,1] => 0 [10,2,2,2] => 3 [10,2,2,1,1] => 0 [10,2,1,1,1,1] => 0 [10,1,1,1,1,1,1] => 0 [9,7] => 0 [9,6,1] => 0 [9,5,2] => 0 [9,5,1,1] => 0 [9,4,3] => 0 [9,4,2,1] => 0 [9,4,1,1,1] => 0 [9,3,3,1] => 3 [9,3,2,2] => 3 [9,3,2,1,1] => 0 [9,3,1,1,1,1] => 0 [9,2,2,2,1] => 0 [9,2,2,1,1,1] => 0 [9,2,1,1,1,1,1] => 0 [9,1,1,1,1,1,1,1] => 0 [8,8] => 0 [8,7,1] => 0 [8,6,2] => 0 [8,6,1,1] => 0 [8,5,3] => 0 [8,5,2,1] => 0 [8,5,1,1,1] => 0 [8,4,4] => 0 [8,4,3,1] => 0 [8,4,2,2] => 3 [8,4,2,1,1] => 0 [8,4,1,1,1,1] => 0 [8,3,3,2] => 0 [8,3,3,1,1] => 3 [8,3,2,2,1] => 0 [8,3,2,1,1,1] => 0 [8,3,1,1,1,1,1] => 0 [8,2,2,2,2] => 0 [8,2,2,2,1,1] => 0 [8,2,2,1,1,1,1] => 0 [8,2,1,1,1,1,1,1] => 0 [8,1,1,1,1,1,1,1,1] => 0 [7,7,2] => 0 [7,7,1,1] => 2 [7,6,3] => 0 [7,6,2,1] => 0 [7,6,1,1,1] => 0 [7,5,4] => 0 [7,5,3,1] => 0 [7,5,2,2] => 3 [7,5,2,1,1] => 0 [7,5,1,1,1,1] => 0 [7,4,4,1] => 3 [7,4,3,2] => 0 [7,4,3,1,1] => 0 [7,4,2,2,1] => 0 [7,4,2,1,1,1] => 0 [7,4,1,1,1,1,1] => 0 [7,3,3,3] => 3 [7,3,3,2,1] => 0 [7,3,3,1,1,1] => 3 [7,3,2,2,2] => 2 [7,3,2,2,1,1] => 0 [7,3,2,1,1,1,1] => 0 [7,3,1,1,1,1,1,1] => 0 [7,2,2,2,2,1] => 0 [7,2,2,2,1,1,1] => 0 [7,2,2,1,1,1,1,1] => 0 [7,2,1,1,1,1,1,1,1] => 0 [7,1,1,1,1,1,1,1,1,1] => 0 [6,6,4] => 2 [6,6,3,1] => 2 [6,6,2,2] => 0 [6,6,2,1,1] => 0 [6,6,1,1,1,1] => 0 [6,5,5] => 0 [6,5,4,1] => 0 [6,5,3,2] => 0 [6,5,3,1,1] => 0 [6,5,2,2,1] => 0 [6,5,2,1,1,1] => 0 [6,5,1,1,1,1,1] => 0 [6,4,4,2] => 0 [6,4,4,1,1] => 3 [6,4,3,3] => 3 [6,4,3,2,1] => 0 [6,4,3,1,1,1] => 0 [6,4,2,2,2] => 2 [6,4,2,2,1,1] => 0 [6,4,2,1,1,1,1] => 0 [6,4,1,1,1,1,1,1] => 0 [6,3,3,3,1] => 3 [6,3,3,2,2] => 0 [6,3,3,2,1,1] => 0 [6,3,3,1,1,1,1] => 3 [6,3,2,2,2,1] => 0 [6,3,2,2,1,1,1] => 0 [6,3,2,1,1,1,1,1] => 0 [6,3,1,1,1,1,1,1,1] => 0 [6,2,2,2,2,2] => 0 [6,2,2,2,2,1,1] => 0 [6,2,2,2,1,1,1,1] => 0 [6,2,2,1,1,1,1,1,1] => 0 [6,2,1,1,1,1,1,1,1,1] => 0 [6,1,1,1,1,1,1,1,1,1,1] => 0 [5,5,5,1] => 0 [5,5,4,2] => 0 [5,5,4,1,1] => 0 [5,5,3,3] => 1 [5,5,3,2,1] => 4 [5,5,3,1,1,1] => 0 [5,5,2,2,2] => 0 [5,5,2,2,1,1] => 2 [5,5,2,1,1,1,1] => 2 [5,5,1,1,1,1,1,1] => 0 [5,4,4,3] => 0 [5,4,4,2,1] => 3 [5,4,4,1,1,1] => 3 [5,4,3,3,1] => 3 [5,4,3,2,2] => 4 [5,4,3,2,1,1] => 0 [5,4,3,1,1,1,1] => 0 [5,4,2,2,2,1] => 0 [5,4,2,2,1,1,1] => 0 [5,4,2,1,1,1,1,1] => 0 [5,4,1,1,1,1,1,1,1] => 0 [5,3,3,3,2] => 0 [5,3,3,3,1,1] => 3 [5,3,3,2,2,1] => 0 [5,3,3,2,1,1,1] => 0 [5,3,3,1,1,1,1,1] => 3 [5,3,2,2,2,2] => 0 [5,3,2,2,2,1,1] => 0 [5,3,2,2,1,1,1,1] => 0 [5,3,2,1,1,1,1,1,1] => 0 [5,3,1,1,1,1,1,1,1,1] => 0 [5,2,2,2,2,2,1] => 0 [5,2,2,2,2,1,1,1] => 0 [5,2,2,2,1,1,1,1,1] => 0 [5,2,2,1,1,1,1,1,1,1] => 0 [5,2,1,1,1,1,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1,1,1,1,1] => 0 [4,4,4,4] => 0 [4,4,4,3,1] => 0 [4,4,4,2,2] => 1 [4,4,4,2,1,1] => 3 [4,4,4,1,1,1,1] => 3 [4,4,3,3,2] => 0 [4,4,3,3,1,1] => 0 [4,4,3,2,2,1] => 0 [4,4,3,2,1,1,1] => 0 [4,4,3,1,1,1,1,1] => 0 [4,4,2,2,2,2] => 0 [4,4,2,2,2,1,1] => 3 [4,4,2,2,1,1,1,1] => 3 [4,4,2,1,1,1,1,1,1] => 3 [4,4,1,1,1,1,1,1,1,1] => 3 [4,3,3,3,3] => 0 [4,3,3,3,2,1] => 0 [4,3,3,3,1,1,1] => 3 [4,3,3,2,2,2] => 2 [4,3,3,2,2,1,1] => 0 [4,3,3,2,1,1,1,1] => 0 [4,3,3,1,1,1,1,1,1] => 3 [4,3,2,2,2,2,1] => 0 [4,3,2,2,2,1,1,1] => 0 [4,3,2,2,1,1,1,1,1] => 0 [4,3,2,1,1,1,1,1,1,1] => 0 [4,3,1,1,1,1,1,1,1,1,1] => 0 [4,2,2,2,2,2,2] => 2 [4,2,2,2,2,2,1,1] => 0 [4,2,2,2,2,1,1,1,1] => 0 [4,2,2,2,1,1,1,1,1,1] => 0 [4,2,2,1,1,1,1,1,1,1,1] => 0 [4,2,1,1,1,1,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,3,3,3,3,1] => 0 [3,3,3,3,2,2] => 2 [3,3,3,3,2,1,1] => 0 [3,3,3,3,1,1,1,1] => 0 [3,3,3,2,2,2,1] => 0 [3,3,3,2,2,1,1,1] => 0 [3,3,3,2,1,1,1,1,1] => 0 [3,3,3,1,1,1,1,1,1,1] => 3 [3,3,2,2,2,2,2] => 0 [3,3,2,2,2,2,1,1] => 0 [3,3,2,2,2,1,1,1,1] => 0 [3,3,2,2,1,1,1,1,1,1] => 0 [3,3,2,1,1,1,1,1,1,1,1] => 0 [3,3,1,1,1,1,1,1,1,1,1,1] => 2 [3,2,2,2,2,2,2,1] => 0 [3,2,2,2,2,2,1,1,1] => 0 [3,2,2,2,2,1,1,1,1,1] => 0 [3,2,2,2,1,1,1,1,1,1,1] => 0 [3,2,2,1,1,1,1,1,1,1,1,1] => 0 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2,2,2] => 0 [2,2,2,2,2,2,2,1,1] => 0 [2,2,2,2,2,2,1,1,1,1] => 0 [2,2,2,2,2,1,1,1,1,1,1] => 0 [2,2,2,2,1,1,1,1,1,1,1,1] => 0 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 0 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [17] => 1 [16,1] => 1 [15,2] => 1 [15,1,1] => 1 [14,3] => 1 [14,2,1] => 1 [14,1,1,1] => 1 [13,4] => 1 [13,3,1] => 1 [13,2,2] => 3 [13,2,1,1] => 1 [13,1,1,1,1] => 1 [12,5] => 1 [12,4,1] => 1 [12,3,2] => 1 [12,3,1,1] => 1 [12,2,2,1] => 1 [12,2,1,1,1] => 1 [12,1,1,1,1,1] => 1 [11,6] => 1 [11,5,1] => 1 [11,4,2] => 1 [11,4,1,1] => 1 [11,3,3] => 2 [11,3,2,1] => 1 [11,3,1,1,1] => 1 [11,2,2,2] => 2 [11,2,2,1,1] => 1 [11,2,1,1,1,1] => 1 [11,1,1,1,1,1,1] => 1 [10,7] => 1 [10,6,1] => 1 [10,5,2] => 1 [10,5,1,1] => 1 [10,4,3] => 1 [10,4,2,1] => 1 [10,4,1,1,1] => 1 [10,3,3,1] => 2 [10,3,2,2] => 2 [10,3,2,1,1] => 1 [10,3,1,1,1,1] => 1 [10,2,2,2,1] => 1 [10,2,2,1,1,1] => 1 [10,2,1,1,1,1,1] => 1 [10,1,1,1,1,1,1,1] => 1 [9,8] => 1 [9,7,1] => 1 [9,6,2] => 1 [9,6,1,1] => 1 [9,5,3] => 1 [9,5,2,1] => 1 [9,5,1,1,1] => 1 [9,4,4] => 1 [9,4,3,1] => 1 [9,4,2,2] => 2 [9,4,2,1,1] => 1 [9,4,1,1,1,1] => 1 [9,3,3,2] => 1 [9,3,3,1,1] => 2 [9,3,2,2,1] => 1 [9,3,2,1,1,1] => 1 [9,3,1,1,1,1,1] => 1 [9,2,2,2,2] => 1 [9,2,2,2,1,1] => 1 [9,2,2,1,1,1,1] => 1 [9,2,1,1,1,1,1,1] => 1 [9,1,1,1,1,1,1,1,1] => 1 [8,8,1] => 2 [8,7,2] => 1 [8,7,1,1] => 1 [8,6,3] => 1 [8,6,2,1] => 1 [8,6,1,1,1] => 1 [8,5,4] => 1 [8,5,3,1] => 1 [8,5,2,2] => 2 [8,5,2,1,1] => 1 [8,5,1,1,1,1] => 1 [8,4,4,1] => 2 [8,4,3,2] => 1 [8,4,3,1,1] => 1 [8,4,2,2,1] => 1 [8,4,2,1,1,1] => 1 [8,4,1,1,1,1,1] => 1 [8,3,3,3] => 2 [8,3,3,2,1] => 1 [8,3,3,1,1,1] => 2 [8,3,2,2,2] => 3 [8,3,2,2,1,1] => 1 [8,3,2,1,1,1,1] => 1 [8,3,1,1,1,1,1,1] => 1 [8,2,2,2,2,1] => 1 [8,2,2,2,1,1,1] => 1 [8,2,2,1,1,1,1,1] => 1 [8,2,1,1,1,1,1,1,1] => 1 [8,1,1,1,1,1,1,1,1,1] => 1 [7,7,3] => 2 [7,7,2,1] => 1 [7,7,1,1,1] => 3 [7,6,4] => 1 [7,6,3,1] => 1 [7,6,2,2] => 2 [7,6,2,1,1] => 1 [7,6,1,1,1,1] => 1 [7,5,5] => 1 [7,5,4,1] => 1 [7,5,3,2] => 1 [7,5,3,1,1] => 1 [7,5,2,2,1] => 1 [7,5,2,1,1,1] => 1 [7,5,1,1,1,1,1] => 1 [7,4,4,2] => 1 [7,4,4,1,1] => 2 [7,4,3,3] => 2 [7,4,3,2,1] => 1 [7,4,3,1,1,1] => 1 [7,4,2,2,2] => 3 [7,4,2,2,1,1] => 1 [7,4,2,1,1,1,1] => 1 [7,4,1,1,1,1,1,1] => 1 [7,3,3,3,1] => 2 [7,3,3,2,2] => 1 [7,3,3,2,1,1] => 1 [7,3,3,1,1,1,1] => 2 [7,3,2,2,2,1] => 1 [7,3,2,2,1,1,1] => 1 [7,3,2,1,1,1,1,1] => 1 [7,3,1,1,1,1,1,1,1] => 1 [7,2,2,2,2,2] => 1 [7,2,2,2,2,1,1] => 1 [7,2,2,2,1,1,1,1] => 1 [7,2,2,1,1,1,1,1,1] => 1 [7,2,1,1,1,1,1,1,1,1] => 1 [7,1,1,1,1,1,1,1,1,1,1] => 1 [6,6,5] => 1 [6,6,4,1] => 1 [6,6,3,2] => 1 [6,6,3,1,1] => 3 [6,6,2,2,1] => 1 [6,6,2,1,1,1] => 1 [6,6,1,1,1,1,1] => 1 [6,5,5,1] => 1 [6,5,4,2] => 1 [6,5,4,1,1] => 1 [6,5,3,3] => 2 [6,5,3,2,1] => 1 [6,5,3,1,1,1] => 1 [6,5,2,2,2] => 3 [6,5,2,2,1,1] => 1 [6,5,2,1,1,1,1] => 1 [6,5,1,1,1,1,1,1] => 1 [6,4,4,3] => 1 [6,4,4,2,1] => 2 [6,4,4,1,1,1] => 2 [6,4,3,3,1] => 2 [6,4,3,2,2] => 3 [6,4,3,2,1,1] => 1 [6,4,3,1,1,1,1] => 1 [6,4,2,2,2,1] => 1 [6,4,2,2,1,1,1] => 1 [6,4,2,1,1,1,1,1] => 1 [6,4,1,1,1,1,1,1,1] => 1 [6,3,3,3,2] => 1 [6,3,3,3,1,1] => 2 [6,3,3,2,2,1] => 1 [6,3,3,2,1,1,1] => 1 [6,3,3,1,1,1,1,1] => 2 [6,3,2,2,2,2] => 1 [6,3,2,2,2,1,1] => 1 [6,3,2,2,1,1,1,1] => 1 [6,3,2,1,1,1,1,1,1] => 1 [6,3,1,1,1,1,1,1,1,1] => 1 [6,2,2,2,2,2,1] => 1 [6,2,2,2,2,1,1,1] => 1 [6,2,2,2,1,1,1,1,1] => 1 [6,2,2,1,1,1,1,1,1,1] => 1 [6,2,1,1,1,1,1,1,1,1,1] => 1 [6,1,1,1,1,1,1,1,1,1,1,1] => 1 [5,5,5,2] => 2 [5,5,5,1,1] => 1 [5,5,4,3] => 2 [5,5,4,2,1] => 1 [5,5,4,1,1,1] => 1 [5,5,3,3,1] => 0 [5,5,3,2,2] => 2 [5,5,3,2,1,1] => 3 [5,5,3,1,1,1,1] => 1 [5,5,2,2,2,1] => 3 [5,5,2,2,1,1,1] => 3 [5,5,2,1,1,1,1,1] => 3 [5,5,1,1,1,1,1,1,1] => 1 [5,4,4,4] => 1 [5,4,4,3,1] => 1 [5,4,4,2,2] => 0 [5,4,4,2,1,1] => 2 [5,4,4,1,1,1,1] => 2 [5,4,3,3,2] => 1 [5,4,3,3,1,1] => 2 [5,4,3,2,2,1] => 1 [5,4,3,2,1,1,1] => 1 [5,4,3,1,1,1,1,1] => 1 [5,4,2,2,2,2] => 1 [5,4,2,2,2,1,1] => 1 [5,4,2,2,1,1,1,1] => 1 [5,4,2,1,1,1,1,1,1] => 1 [5,4,1,1,1,1,1,1,1,1] => 1 [5,3,3,3,3] => 1 [5,3,3,3,2,1] => 1 [5,3,3,3,1,1,1] => 2 [5,3,3,2,2,2] => 3 [5,3,3,2,2,1,1] => 1 [5,3,3,2,1,1,1,1] => 1 [5,3,3,1,1,1,1,1,1] => 2 [5,3,2,2,2,2,1] => 1 [5,3,2,2,2,1,1,1] => 1 [5,3,2,2,1,1,1,1,1] => 1 [5,3,2,1,1,1,1,1,1,1] => 1 [5,3,1,1,1,1,1,1,1,1,1] => 1 [5,2,2,2,2,2,2] => 3 [5,2,2,2,2,2,1,1] => 1 [5,2,2,2,2,1,1,1,1] => 1 [5,2,2,2,1,1,1,1,1,1] => 1 [5,2,2,1,1,1,1,1,1,1,1] => 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 [4,4,4,4,1] => 1 [4,4,4,3,2] => 2 [4,4,4,3,1,1] => 1 [4,4,4,2,2,1] => 2 [4,4,4,2,1,1,1] => 2 [4,4,4,1,1,1,1,1] => 2 [4,4,3,3,3] => 2 [4,4,3,3,2,1] => 1 [4,4,3,3,1,1,1] => 1 [4,4,3,2,2,2] => 1 [4,4,3,2,2,1,1] => 1 [4,4,3,2,1,1,1,1] => 1 [4,4,3,1,1,1,1,1,1] => 1 [4,4,2,2,2,2,1] => 2 [4,4,2,2,2,1,1,1] => 2 [4,4,2,2,1,1,1,1,1] => 2 [4,4,2,1,1,1,1,1,1,1] => 2 [4,4,1,1,1,1,1,1,1,1,1] => 2 [4,3,3,3,3,1] => 1 [4,3,3,3,2,2] => 1 [4,3,3,3,2,1,1] => 1 [4,3,3,3,1,1,1,1] => 2 [4,3,3,2,2,2,1] => 1 [4,3,3,2,2,1,1,1] => 1 [4,3,3,2,1,1,1,1,1] => 1 [4,3,3,1,1,1,1,1,1,1] => 2 [4,3,2,2,2,2,2] => 1 [4,3,2,2,2,2,1,1] => 1 [4,3,2,2,2,1,1,1,1] => 1 [4,3,2,2,1,1,1,1,1,1] => 1 [4,3,2,1,1,1,1,1,1,1,1] => 1 [4,3,1,1,1,1,1,1,1,1,1,1] => 1 [4,2,2,2,2,2,2,1] => 1 [4,2,2,2,2,2,1,1,1] => 1 [4,2,2,2,2,1,1,1,1,1] => 1 [4,2,2,2,1,1,1,1,1,1,1] => 1 [4,2,2,1,1,1,1,1,1,1,1,1] => 1 [4,2,1,1,1,1,1,1,1,1,1,1,1] => 1 [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [3,3,3,3,3,2] => 1 [3,3,3,3,3,1,1] => 1 [3,3,3,3,2,2,1] => 1 [3,3,3,3,2,1,1,1] => 1 [3,3,3,3,1,1,1,1,1] => 1 [3,3,3,2,2,2,2] => 2 [3,3,3,2,2,2,1,1] => 1 [3,3,3,2,2,1,1,1,1] => 1 [3,3,3,2,1,1,1,1,1,1] => 1 [3,3,3,1,1,1,1,1,1,1,1] => 2 [3,3,2,2,2,2,2,1] => 1 [3,3,2,2,2,2,1,1,1] => 1 [3,3,2,2,2,1,1,1,1,1] => 1 [3,3,2,2,1,1,1,1,1,1,1] => 1 [3,3,2,1,1,1,1,1,1,1,1,1] => 1 [3,3,1,1,1,1,1,1,1,1,1,1,1] => 3 [3,2,2,2,2,2,2,2] => 2 [3,2,2,2,2,2,2,1,1] => 1 [3,2,2,2,2,2,1,1,1,1] => 1 [3,2,2,2,2,1,1,1,1,1,1] => 1 [3,2,2,2,1,1,1,1,1,1,1,1] => 1 [3,2,2,1,1,1,1,1,1,1,1,1,1] => 1 ----------------------------------------------------------------------------- Created: Jun 20, 2013 at 19:29 by Per Alexandersson ----------------------------------------------------------------------------- Last Updated: Dec 29, 2016 at 09:10 by Christian Stump