***************************************************************************** * 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: St000118 ----------------------------------------------------------------------------- Collection: Binary trees ----------------------------------------------------------------------------- Description: The number of occurrences of the contiguous pattern {{{[.,[.,[.,.]]]}}} in a binary tree. [[oeis:A001006]] counts binary trees avoiding this pattern. ----------------------------------------------------------------------------- References: [1] Donaghey, R., Shapiro, L. W. Motzkin numbers [[MathSciNet:0505544]] [2] Rowland, E. S. Pattern avoidance in binary trees [[MathSciNet:2645188]] [[arXiv:0809.0488]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [.,.] => 0 [.,[.,.]] => 0 [[.,.],.] => 0 [.,[.,[.,.]]] => 1 [.,[[.,.],.]] => 0 [[.,.],[.,.]] => 0 [[.,[.,.]],.] => 0 [[[.,.],.],.] => 0 [.,[.,[.,[.,.]]]] => 2 [.,[.,[[.,.],.]]] => 1 [.,[[.,.],[.,.]]] => 1 [.,[[.,[.,.]],.]] => 0 [.,[[[.,.],.],.]] => 0 [[.,.],[.,[.,.]]] => 1 [[.,.],[[.,.],.]] => 0 [[.,[.,.]],[.,.]] => 0 [[[.,.],.],[.,.]] => 0 [[.,[.,[.,.]]],.] => 1 [[.,[[.,.],.]],.] => 0 [[[.,.],[.,.]],.] => 0 [[[.,[.,.]],.],.] => 0 [[[[.,.],.],.],.] => 0 [.,[.,[.,[.,[.,.]]]]] => 3 [.,[.,[.,[[.,.],.]]]] => 2 [.,[.,[[.,.],[.,.]]]] => 2 [.,[.,[[.,[.,.]],.]]] => 1 [.,[.,[[[.,.],.],.]]] => 1 [.,[[.,.],[.,[.,.]]]] => 2 [.,[[.,.],[[.,.],.]]] => 1 [.,[[.,[.,.]],[.,.]]] => 1 [.,[[[.,.],.],[.,.]]] => 1 [.,[[.,[.,[.,.]]],.]] => 1 [.,[[.,[[.,.],.]],.]] => 0 [.,[[[.,.],[.,.]],.]] => 0 [.,[[[.,[.,.]],.],.]] => 0 [.,[[[[.,.],.],.],.]] => 0 [[.,.],[.,[.,[.,.]]]] => 2 [[.,.],[.,[[.,.],.]]] => 1 [[.,.],[[.,.],[.,.]]] => 1 [[.,.],[[.,[.,.]],.]] => 0 [[.,.],[[[.,.],.],.]] => 0 [[.,[.,.]],[.,[.,.]]] => 1 [[.,[.,.]],[[.,.],.]] => 0 [[[.,.],.],[.,[.,.]]] => 1 [[[.,.],.],[[.,.],.]] => 0 [[.,[.,[.,.]]],[.,.]] => 1 [[.,[[.,.],.]],[.,.]] => 0 [[[.,.],[.,.]],[.,.]] => 0 [[[.,[.,.]],.],[.,.]] => 0 [[[[.,.],.],.],[.,.]] => 0 [[.,[.,[.,[.,.]]]],.] => 2 [[.,[.,[[.,.],.]]],.] => 1 [[.,[[.,.],[.,.]]],.] => 1 [[.,[[.,[.,.]],.]],.] => 0 [[.,[[[.,.],.],.]],.] => 0 [[[.,.],[.,[.,.]]],.] => 1 [[[.,.],[[.,.],.]],.] => 0 [[[.,[.,.]],[.,.]],.] => 0 [[[[.,.],.],[.,.]],.] => 0 [[[.,[.,[.,.]]],.],.] => 1 [[[.,[[.,.],.]],.],.] => 0 [[[[.,.],[.,.]],.],.] => 0 [[[[.,[.,.]],.],.],.] => 0 [[[[[.,.],.],.],.],.] => 0 [.,[.,[.,[.,[.,[.,.]]]]]] => 4 [.,[.,[.,[.,[[.,.],.]]]]] => 3 [.,[.,[.,[[.,.],[.,.]]]]] => 3 [.,[.,[.,[[.,[.,.]],.]]]] => 2 [.,[.,[.,[[[.,.],.],.]]]] => 2 [.,[.,[[.,.],[.,[.,.]]]]] => 3 [.,[.,[[.,.],[[.,.],.]]]] => 2 [.,[.,[[.,[.,.]],[.,.]]]] => 2 [.,[.,[[[.,.],.],[.,.]]]] => 2 [.,[.,[[.,[.,[.,.]]],.]]] => 2 [.,[.,[[.,[[.,.],.]],.]]] => 1 [.,[.,[[[.,.],[.,.]],.]]] => 1 [.,[.,[[[.,[.,.]],.],.]]] => 1 [.,[.,[[[[.,.],.],.],.]]] => 1 [.,[[.,.],[.,[.,[.,.]]]]] => 3 [.,[[.,.],[.,[[.,.],.]]]] => 2 [.,[[.,.],[[.,.],[.,.]]]] => 2 [.,[[.,.],[[.,[.,.]],.]]] => 1 [.,[[.,.],[[[.,.],.],.]]] => 1 [.,[[.,[.,.]],[.,[.,.]]]] => 2 [.,[[.,[.,.]],[[.,.],.]]] => 1 [.,[[[.,.],.],[.,[.,.]]]] => 2 [.,[[[.,.],.],[[.,.],.]]] => 1 [.,[[.,[.,[.,.]]],[.,.]]] => 2 [.,[[.,[[.,.],.]],[.,.]]] => 1 [.,[[[.,.],[.,.]],[.,.]]] => 1 [.,[[[.,[.,.]],.],[.,.]]] => 1 [.,[[[[.,.],.],.],[.,.]]] => 1 [.,[[.,[.,[.,[.,.]]]],.]] => 2 [.,[[.,[.,[[.,.],.]]],.]] => 1 [.,[[.,[[.,.],[.,.]]],.]] => 1 [.,[[.,[[.,[.,.]],.]],.]] => 0 [.,[[.,[[[.,.],.],.]],.]] => 0 [.,[[[.,.],[.,[.,.]]],.]] => 1 [.,[[[.,.],[[.,.],.]],.]] => 0 [.,[[[.,[.,.]],[.,.]],.]] => 0 [.,[[[[.,.],.],[.,.]],.]] => 0 [.,[[[.,[.,[.,.]]],.],.]] => 1 [.,[[[.,[[.,.],.]],.],.]] => 0 [.,[[[[.,.],[.,.]],.],.]] => 0 [.,[[[[.,[.,.]],.],.],.]] => 0 [.,[[[[[.,.],.],.],.],.]] => 0 [[.,.],[.,[.,[.,[.,.]]]]] => 3 [[.,.],[.,[.,[[.,.],.]]]] => 2 [[.,.],[.,[[.,.],[.,.]]]] => 2 [[.,.],[.,[[.,[.,.]],.]]] => 1 [[.,.],[.,[[[.,.],.],.]]] => 1 [[.,.],[[.,.],[.,[.,.]]]] => 2 [[.,.],[[.,.],[[.,.],.]]] => 1 [[.,.],[[.,[.,.]],[.,.]]] => 1 [[.,.],[[[.,.],.],[.,.]]] => 1 [[.,.],[[.,[.,[.,.]]],.]] => 1 [[.,.],[[.,[[.,.],.]],.]] => 0 [[.,.],[[[.,.],[.,.]],.]] => 0 [[.,.],[[[.,[.,.]],.],.]] => 0 [[.,.],[[[[.,.],.],.],.]] => 0 [[.,[.,.]],[.,[.,[.,.]]]] => 2 [[.,[.,.]],[.,[[.,.],.]]] => 1 [[.,[.,.]],[[.,.],[.,.]]] => 1 [[.,[.,.]],[[.,[.,.]],.]] => 0 [[.,[.,.]],[[[.,.],.],.]] => 0 [[[.,.],.],[.,[.,[.,.]]]] => 2 [[[.,.],.],[.,[[.,.],.]]] => 1 [[[.,.],.],[[.,.],[.,.]]] => 1 [[[.,.],.],[[.,[.,.]],.]] => 0 [[[.,.],.],[[[.,.],.],.]] => 0 [[.,[.,[.,.]]],[.,[.,.]]] => 2 [[.,[.,[.,.]]],[[.,.],.]] => 1 [[.,[[.,.],.]],[.,[.,.]]] => 1 [[.,[[.,.],.]],[[.,.],.]] => 0 [[[.,.],[.,.]],[.,[.,.]]] => 1 [[[.,.],[.,.]],[[.,.],.]] => 0 [[[.,[.,.]],.],[.,[.,.]]] => 1 [[[.,[.,.]],.],[[.,.],.]] => 0 [[[[.,.],.],.],[.,[.,.]]] => 1 [[[[.,.],.],.],[[.,.],.]] => 0 [[.,[.,[.,[.,.]]]],[.,.]] => 2 [[.,[.,[[.,.],.]]],[.,.]] => 1 [[.,[[.,.],[.,.]]],[.,.]] => 1 [[.,[[.,[.,.]],.]],[.,.]] => 0 [[.,[[[.,.],.],.]],[.,.]] => 0 [[[.,.],[.,[.,.]]],[.,.]] => 1 [[[.,.],[[.,.],.]],[.,.]] => 0 [[[.,[.,.]],[.,.]],[.,.]] => 0 [[[[.,.],.],[.,.]],[.,.]] => 0 [[[.,[.,[.,.]]],.],[.,.]] => 1 [[[.,[[.,.],.]],.],[.,.]] => 0 [[[[.,.],[.,.]],.],[.,.]] => 0 [[[[.,[.,.]],.],.],[.,.]] => 0 [[[[[.,.],.],.],.],[.,.]] => 0 [[.,[.,[.,[.,[.,.]]]]],.] => 3 [[.,[.,[.,[[.,.],.]]]],.] => 2 [[.,[.,[[.,.],[.,.]]]],.] => 2 [[.,[.,[[.,[.,.]],.]]],.] => 1 [[.,[.,[[[.,.],.],.]]],.] => 1 [[.,[[.,.],[.,[.,.]]]],.] => 2 [[.,[[.,.],[[.,.],.]]],.] => 1 [[.,[[.,[.,.]],[.,.]]],.] => 1 [[.,[[[.,.],.],[.,.]]],.] => 1 [[.,[[.,[.,[.,.]]],.]],.] => 1 [[.,[[.,[[.,.],.]],.]],.] => 0 [[.,[[[.,.],[.,.]],.]],.] => 0 [[.,[[[.,[.,.]],.],.]],.] => 0 [[.,[[[[.,.],.],.],.]],.] => 0 [[[.,.],[.,[.,[.,.]]]],.] => 2 [[[.,.],[.,[[.,.],.]]],.] => 1 [[[.,.],[[.,.],[.,.]]],.] => 1 [[[.,.],[[.,[.,.]],.]],.] => 0 [[[.,.],[[[.,.],.],.]],.] => 0 [[[.,[.,.]],[.,[.,.]]],.] => 1 [[[.,[.,.]],[[.,.],.]],.] => 0 [[[[.,.],.],[.,[.,.]]],.] => 1 [[[[.,.],.],[[.,.],.]],.] => 0 [[[.,[.,[.,.]]],[.,.]],.] => 1 [[[.,[[.,.],.]],[.,.]],.] => 0 [[[[.,.],[.,.]],[.,.]],.] => 0 [[[[.,[.,.]],.],[.,.]],.] => 0 [[[[[.,.],.],.],[.,.]],.] => 0 [[[.,[.,[.,[.,.]]]],.],.] => 2 [[[.,[.,[[.,.],.]]],.],.] => 1 [[[.,[[.,.],[.,.]]],.],.] => 1 [[[.,[[.,[.,.]],.]],.],.] => 0 [[[.,[[[.,.],.],.]],.],.] => 0 [[[[.,.],[.,[.,.]]],.],.] => 1 [[[[.,.],[[.,.],.]],.],.] => 0 [[[[.,[.,.]],[.,.]],.],.] => 0 [[[[[.,.],.],[.,.]],.],.] => 0 [[[[.,[.,[.,.]]],.],.],.] => 1 [[[[.,[[.,.],.]],.],.],.] => 0 [[[[[.,.],[.,.]],.],.],.] => 0 [[[[[.,[.,.]],.],.],.],.] => 0 [[[[[[.,.],.],.],.],.],.] => 0 [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 5 [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 4 [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 4 [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 3 [.,[.,[.,[.,[[[.,.],.],.]]]]] => 3 [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 4 [.,[.,[.,[[.,.],[[.,.],.]]]]] => 3 [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 3 [.,[.,[.,[[[.,.],.],[.,.]]]]] => 3 [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 3 [.,[.,[.,[[.,[[.,.],.]],.]]]] => 2 [.,[.,[.,[[[.,.],[.,.]],.]]]] => 2 [.,[.,[.,[[[.,[.,.]],.],.]]]] => 2 [.,[.,[.,[[[[.,.],.],.],.]]]] => 2 [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 4 [.,[.,[[.,.],[.,[[.,.],.]]]]] => 3 [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3 [.,[.,[[.,.],[[.,[.,.]],.]]]] => 2 [.,[.,[[.,.],[[[.,.],.],.]]]] => 2 [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 3 [.,[.,[[.,[.,.]],[[.,.],.]]]] => 2 [.,[.,[[[.,.],.],[.,[.,.]]]]] => 3 [.,[.,[[[.,.],.],[[.,.],.]]]] => 2 [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 3 [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2 [.,[.,[[[.,.],[.,.]],[.,.]]]] => 2 [.,[.,[[[.,[.,.]],.],[.,.]]]] => 2 [.,[.,[[[[.,.],.],.],[.,.]]]] => 2 [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 3 [.,[.,[[.,[.,[[.,.],.]]],.]]] => 2 [.,[.,[[.,[[.,.],[.,.]]],.]]] => 2 [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1 [.,[.,[[.,[[[.,.],.],.]],.]]] => 1 [.,[.,[[[.,.],[.,[.,.]]],.]]] => 2 [.,[.,[[[.,.],[[.,.],.]],.]]] => 1 [.,[.,[[[.,[.,.]],[.,.]],.]]] => 1 [.,[.,[[[[.,.],.],[.,.]],.]]] => 1 [.,[.,[[[.,[.,[.,.]]],.],.]]] => 2 [.,[.,[[[.,[[.,.],.]],.],.]]] => 1 [.,[.,[[[[.,.],[.,.]],.],.]]] => 1 [.,[.,[[[[.,[.,.]],.],.],.]]] => 1 [.,[.,[[[[[.,.],.],.],.],.]]] => 1 [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 4 [.,[[.,.],[.,[.,[[.,.],.]]]]] => 3 [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3 [.,[[.,.],[.,[[.,[.,.]],.]]]] => 2 [.,[[.,.],[.,[[[.,.],.],.]]]] => 2 [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3 [.,[[.,.],[[.,.],[[.,.],.]]]] => 2 [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2 [.,[[.,.],[[[.,.],.],[.,.]]]] => 2 [.,[[.,.],[[.,[.,[.,.]]],.]]] => 2 [.,[[.,.],[[.,[[.,.],.]],.]]] => 1 [.,[[.,.],[[[.,.],[.,.]],.]]] => 1 [.,[[.,.],[[[.,[.,.]],.],.]]] => 1 [.,[[.,.],[[[[.,.],.],.],.]]] => 1 [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 3 [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2 [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2 [.,[[.,[.,.]],[[.,[.,.]],.]]] => 1 [.,[[.,[.,.]],[[[.,.],.],.]]] => 1 [.,[[[.,.],.],[.,[.,[.,.]]]]] => 3 [.,[[[.,.],.],[.,[[.,.],.]]]] => 2 [.,[[[.,.],.],[[.,.],[.,.]]]] => 2 [.,[[[.,.],.],[[.,[.,.]],.]]] => 1 [.,[[[.,.],.],[[[.,.],.],.]]] => 1 [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 3 [.,[[.,[.,[.,.]]],[[.,.],.]]] => 2 [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2 [.,[[.,[[.,.],.]],[[.,.],.]]] => 1 [.,[[[.,.],[.,.]],[.,[.,.]]]] => 2 [.,[[[.,.],[.,.]],[[.,.],.]]] => 1 [.,[[[.,[.,.]],.],[.,[.,.]]]] => 2 [.,[[[.,[.,.]],.],[[.,.],.]]] => 1 [.,[[[[.,.],.],.],[.,[.,.]]]] => 2 [.,[[[[.,.],.],.],[[.,.],.]]] => 1 [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 3 [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2 [.,[[.,[[.,.],[.,.]]],[.,.]]] => 2 [.,[[.,[[.,[.,.]],.]],[.,.]]] => 1 [.,[[.,[[[.,.],.],.]],[.,.]]] => 1 [.,[[[.,.],[.,[.,.]]],[.,.]]] => 2 [.,[[[.,.],[[.,.],.]],[.,.]]] => 1 [.,[[[.,[.,.]],[.,.]],[.,.]]] => 1 [.,[[[[.,.],.],[.,.]],[.,.]]] => 1 [.,[[[.,[.,[.,.]]],.],[.,.]]] => 2 [.,[[[.,[[.,.],.]],.],[.,.]]] => 1 [.,[[[[.,.],[.,.]],.],[.,.]]] => 1 [.,[[[[.,[.,.]],.],.],[.,.]]] => 1 [.,[[[[[.,.],.],.],.],[.,.]]] => 1 [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 3 [.,[[.,[.,[.,[[.,.],.]]]],.]] => 2 [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2 [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1 [.,[[.,[.,[[[.,.],.],.]]],.]] => 1 [.,[[.,[[.,.],[.,[.,.]]]],.]] => 2 [.,[[.,[[.,.],[[.,.],.]]],.]] => 1 [.,[[.,[[.,[.,.]],[.,.]]],.]] => 1 [.,[[.,[[[.,.],.],[.,.]]],.]] => 1 [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1 [.,[[.,[[.,[[.,.],.]],.]],.]] => 0 [.,[[.,[[[.,.],[.,.]],.]],.]] => 0 [.,[[.,[[[.,[.,.]],.],.]],.]] => 0 [.,[[.,[[[[.,.],.],.],.]],.]] => 0 [.,[[[.,.],[.,[.,[.,.]]]],.]] => 2 [.,[[[.,.],[.,[[.,.],.]]],.]] => 1 [.,[[[.,.],[[.,.],[.,.]]],.]] => 1 [.,[[[.,.],[[.,[.,.]],.]],.]] => 0 [.,[[[.,.],[[[.,.],.],.]],.]] => 0 [.,[[[.,[.,.]],[.,[.,.]]],.]] => 1 [.,[[[.,[.,.]],[[.,.],.]],.]] => 0 [.,[[[[.,.],.],[.,[.,.]]],.]] => 1 [.,[[[[.,.],.],[[.,.],.]],.]] => 0 [.,[[[.,[.,[.,.]]],[.,.]],.]] => 1 [.,[[[.,[[.,.],.]],[.,.]],.]] => 0 [.,[[[[.,.],[.,.]],[.,.]],.]] => 0 [.,[[[[.,[.,.]],.],[.,.]],.]] => 0 [.,[[[[[.,.],.],.],[.,.]],.]] => 0 [.,[[[.,[.,[.,[.,.]]]],.],.]] => 2 [.,[[[.,[.,[[.,.],.]]],.],.]] => 1 [.,[[[.,[[.,.],[.,.]]],.],.]] => 1 [.,[[[.,[[.,[.,.]],.]],.],.]] => 0 [.,[[[.,[[[.,.],.],.]],.],.]] => 0 [.,[[[[.,.],[.,[.,.]]],.],.]] => 1 [.,[[[[.,.],[[.,.],.]],.],.]] => 0 [.,[[[[.,[.,.]],[.,.]],.],.]] => 0 [.,[[[[[.,.],.],[.,.]],.],.]] => 0 [.,[[[[.,[.,[.,.]]],.],.],.]] => 1 [.,[[[[.,[[.,.],.]],.],.],.]] => 0 [.,[[[[[.,.],[.,.]],.],.],.]] => 0 [.,[[[[[.,[.,.]],.],.],.],.]] => 0 [.,[[[[[[.,.],.],.],.],.],.]] => 0 [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 4 [[.,.],[.,[.,[.,[[.,.],.]]]]] => 3 [[.,.],[.,[.,[[.,.],[.,.]]]]] => 3 [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2 [[.,.],[.,[.,[[[.,.],.],.]]]] => 2 [[.,.],[.,[[.,.],[.,[.,.]]]]] => 3 [[.,.],[.,[[.,.],[[.,.],.]]]] => 2 [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2 [[.,.],[.,[[[.,.],.],[.,.]]]] => 2 [[.,.],[.,[[.,[.,[.,.]]],.]]] => 2 [[.,.],[.,[[.,[[.,.],.]],.]]] => 1 [[.,.],[.,[[[.,.],[.,.]],.]]] => 1 [[.,.],[.,[[[.,[.,.]],.],.]]] => 1 [[.,.],[.,[[[[.,.],.],.],.]]] => 1 [[.,.],[[.,.],[.,[.,[.,.]]]]] => 3 [[.,.],[[.,.],[.,[[.,.],.]]]] => 2 [[.,.],[[.,.],[[.,.],[.,.]]]] => 2 [[.,.],[[.,.],[[.,[.,.]],.]]] => 1 [[.,.],[[.,.],[[[.,.],.],.]]] => 1 [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2 [[.,.],[[.,[.,.]],[[.,.],.]]] => 1 [[.,.],[[[.,.],.],[.,[.,.]]]] => 2 [[.,.],[[[.,.],.],[[.,.],.]]] => 1 [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2 [[.,.],[[.,[[.,.],.]],[.,.]]] => 1 [[.,.],[[[.,.],[.,.]],[.,.]]] => 1 [[.,.],[[[.,[.,.]],.],[.,.]]] => 1 [[.,.],[[[[.,.],.],.],[.,.]]] => 1 [[.,.],[[.,[.,[.,[.,.]]]],.]] => 2 [[.,.],[[.,[.,[[.,.],.]]],.]] => 1 [[.,.],[[.,[[.,.],[.,.]]],.]] => 1 [[.,.],[[.,[[.,[.,.]],.]],.]] => 0 [[.,.],[[.,[[[.,.],.],.]],.]] => 0 [[.,.],[[[.,.],[.,[.,.]]],.]] => 1 [[.,.],[[[.,.],[[.,.],.]],.]] => 0 [[.,.],[[[.,[.,.]],[.,.]],.]] => 0 [[.,.],[[[[.,.],.],[.,.]],.]] => 0 [[.,.],[[[.,[.,[.,.]]],.],.]] => 1 [[.,.],[[[.,[[.,.],.]],.],.]] => 0 [[.,.],[[[[.,.],[.,.]],.],.]] => 0 [[.,.],[[[[.,[.,.]],.],.],.]] => 0 [[.,.],[[[[[.,.],.],.],.],.]] => 0 [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 3 [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2 [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2 [[.,[.,.]],[.,[[.,[.,.]],.]]] => 1 [[.,[.,.]],[.,[[[.,.],.],.]]] => 1 [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2 [[.,[.,.]],[[.,.],[[.,.],.]]] => 1 [[.,[.,.]],[[.,[.,.]],[.,.]]] => 1 [[.,[.,.]],[[[.,.],.],[.,.]]] => 1 [[.,[.,.]],[[.,[.,[.,.]]],.]] => 1 [[.,[.,.]],[[.,[[.,.],.]],.]] => 0 [[.,[.,.]],[[[.,.],[.,.]],.]] => 0 [[.,[.,.]],[[[.,[.,.]],.],.]] => 0 [[.,[.,.]],[[[[.,.],.],.],.]] => 0 [[[.,.],.],[.,[.,[.,[.,.]]]]] => 3 [[[.,.],.],[.,[.,[[.,.],.]]]] => 2 [[[.,.],.],[.,[[.,.],[.,.]]]] => 2 [[[.,.],.],[.,[[.,[.,.]],.]]] => 1 [[[.,.],.],[.,[[[.,.],.],.]]] => 1 [[[.,.],.],[[.,.],[.,[.,.]]]] => 2 [[[.,.],.],[[.,.],[[.,.],.]]] => 1 [[[.,.],.],[[.,[.,.]],[.,.]]] => 1 [[[.,.],.],[[[.,.],.],[.,.]]] => 1 [[[.,.],.],[[.,[.,[.,.]]],.]] => 1 [[[.,.],.],[[.,[[.,.],.]],.]] => 0 [[[.,.],.],[[[.,.],[.,.]],.]] => 0 [[[.,.],.],[[[.,[.,.]],.],.]] => 0 [[[.,.],.],[[[[.,.],.],.],.]] => 0 [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 3 [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2 [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2 [[.,[.,[.,.]]],[[.,[.,.]],.]] => 1 [[.,[.,[.,.]]],[[[.,.],.],.]] => 1 [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2 [[.,[[.,.],.]],[.,[[.,.],.]]] => 1 [[.,[[.,.],.]],[[.,.],[.,.]]] => 1 [[.,[[.,.],.]],[[.,[.,.]],.]] => 0 [[.,[[.,.],.]],[[[.,.],.],.]] => 0 [[[.,.],[.,.]],[.,[.,[.,.]]]] => 2 [[[.,.],[.,.]],[.,[[.,.],.]]] => 1 [[[.,.],[.,.]],[[.,.],[.,.]]] => 1 [[[.,.],[.,.]],[[.,[.,.]],.]] => 0 [[[.,.],[.,.]],[[[.,.],.],.]] => 0 [[[.,[.,.]],.],[.,[.,[.,.]]]] => 2 [[[.,[.,.]],.],[.,[[.,.],.]]] => 1 [[[.,[.,.]],.],[[.,.],[.,.]]] => 1 [[[.,[.,.]],.],[[.,[.,.]],.]] => 0 [[[.,[.,.]],.],[[[.,.],.],.]] => 0 [[[[.,.],.],.],[.,[.,[.,.]]]] => 2 [[[[.,.],.],.],[.,[[.,.],.]]] => 1 [[[[.,.],.],.],[[.,.],[.,.]]] => 1 [[[[.,.],.],.],[[.,[.,.]],.]] => 0 [[[[.,.],.],.],[[[.,.],.],.]] => 0 [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 3 [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2 [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2 [[.,[.,[[.,.],.]]],[[.,.],.]] => 1 [[.,[[.,.],[.,.]]],[.,[.,.]]] => 2 [[.,[[.,.],[.,.]]],[[.,.],.]] => 1 [[.,[[.,[.,.]],.]],[.,[.,.]]] => 1 [[.,[[.,[.,.]],.]],[[.,.],.]] => 0 [[.,[[[.,.],.],.]],[.,[.,.]]] => 1 [[.,[[[.,.],.],.]],[[.,.],.]] => 0 [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2 [[[.,.],[.,[.,.]]],[[.,.],.]] => 1 [[[.,.],[[.,.],.]],[.,[.,.]]] => 1 [[[.,.],[[.,.],.]],[[.,.],.]] => 0 [[[.,[.,.]],[.,.]],[.,[.,.]]] => 1 [[[.,[.,.]],[.,.]],[[.,.],.]] => 0 [[[[.,.],.],[.,.]],[.,[.,.]]] => 1 [[[[.,.],.],[.,.]],[[.,.],.]] => 0 [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2 [[[.,[.,[.,.]]],.],[[.,.],.]] => 1 [[[.,[[.,.],.]],.],[.,[.,.]]] => 1 [[[.,[[.,.],.]],.],[[.,.],.]] => 0 [[[[.,.],[.,.]],.],[.,[.,.]]] => 1 [[[[.,.],[.,.]],.],[[.,.],.]] => 0 [[[[.,[.,.]],.],.],[.,[.,.]]] => 1 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[[[[[.,.],[.,[.,.]]],.],.],.] => 1 [[[[[.,.],[[.,.],.]],.],.],.] => 0 [[[[[.,[.,.]],[.,.]],.],.],.] => 0 [[[[[[.,.],.],[.,.]],.],.],.] => 0 [[[[[.,[.,[.,.]]],.],.],.],.] => 1 [[[[[.,[[.,.],.]],.],.],.],.] => 0 [[[[[[.,.],[.,.]],.],.],.],.] => 0 [[[[[[.,[.,.]],.],.],.],.],.] => 0 [[[[[[[.,.],.],.],.],.],.],.] => 0 ----------------------------------------------------------------------------- Created: Jun 18, 2013 at 16:59 by Eric Rowland ----------------------------------------------------------------------------- Last Updated: Oct 17, 2015 at 11:05 by Christian Stump