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[[.,.],[[[[.,[.,.]],.],.],.]] generating graphics... => 0
[[.,.],[[[[[.,.],.],.],.],.]] generating graphics... => 0
[[.,[.,.]],[.,[.,[.,[.,.]]]]] generating graphics... => 0
[[.,[.,.]],[.,[.,[[.,.],.]]]] generating graphics... => 0
[[.,[.,.]],[.,[[.,.],[.,.]]]] generating graphics... => 0
[[.,[.,.]],[.,[[.,[.,.]],.]]] generating graphics... => 1
[[.,[.,.]],[.,[[[.,.],.],.]]] generating graphics... => 0
[[.,[.,.]],[[.,.],[.,[.,.]]]] generating graphics... => 0
[[.,[.,.]],[[.,.],[[.,.],.]]] generating graphics... => 0
[[.,[.,.]],[[.,[.,.]],[.,.]]] generating graphics... => 0
[[.,[.,.]],[[[.,.],.],[.,.]]] generating graphics... => 0
[[.,[.,.]],[[.,[.,[.,.]]],.]] generating graphics... => 0
[[.,[.,.]],[[.,[[.,.],.]],.]] generating graphics... => 0
[[.,[.,.]],[[[.,.],[.,.]],.]] generating graphics... => 0
[[.,[.,.]],[[[.,[.,.]],.],.]] generating graphics... => 0
[[.,[.,.]],[[[[.,.],.],.],.]] generating graphics... => 0
[[[.,.],.],[.,[.,[.,[.,.]]]]] generating graphics... => 0
[[[.,.],.],[.,[.,[[.,.],.]]]] generating graphics... => 0
[[[.,.],.],[.,[[.,.],[.,.]]]] generating graphics... => 0
[[[.,.],.],[.,[[.,[.,.]],.]]] generating graphics... => 1
[[[.,.],.],[.,[[[.,.],.],.]]] generating graphics... => 0
[[[.,.],.],[[.,.],[.,[.,.]]]] generating graphics... => 0
[[[.,.],.],[[.,.],[[.,.],.]]] generating graphics... => 0
[[[.,.],.],[[.,[.,.]],[.,.]]] generating graphics... => 0
[[[.,.],.],[[[.,.],.],[.,.]]] generating graphics... => 0
[[[.,.],.],[[.,[.,[.,.]]],.]] generating graphics... => 0
[[[.,.],.],[[.,[[.,.],.]],.]] generating graphics... => 0
[[[.,.],.],[[[.,.],[.,.]],.]] generating graphics... => 0
[[[.,.],.],[[[.,[.,.]],.],.]] generating graphics... => 0
[[[.,.],.],[[[[.,.],.],.],.]] generating graphics... => 0
[[.,[.,[.,.]]],[.,[.,[.,.]]]] generating graphics... => 0
[[.,[.,[.,.]]],[.,[[.,.],.]]] generating graphics... => 0
[[.,[.,[.,.]]],[[.,.],[.,.]]] generating graphics... => 0
[[.,[.,[.,.]]],[[.,[.,.]],.]] generating graphics... => 0
[[.,[.,[.,.]]],[[[.,.],.],.]] generating graphics... => 0
[[.,[[.,.],.]],[.,[.,[.,.]]]] generating graphics... => 0
[[.,[[.,.],.]],[.,[[.,.],.]]] generating graphics... => 0
[[.,[[.,.],.]],[[.,.],[.,.]]] generating graphics... => 0
[[.,[[.,.],.]],[[.,[.,.]],.]] generating graphics... => 0
[[.,[[.,.],.]],[[[.,.],.],.]] generating graphics... => 0
[[[.,.],[.,.]],[.,[.,[.,.]]]] generating graphics... => 0
[[[.,.],[.,.]],[.,[[.,.],.]]] generating graphics... => 0
[[[.,.],[.,.]],[[.,.],[.,.]]] generating graphics... => 0
[[[.,.],[.,.]],[[.,[.,.]],.]] generating graphics... => 0
[[[.,.],[.,.]],[[[.,.],.],.]] generating graphics... => 0
[[[.,[.,.]],.],[.,[.,[.,.]]]] generating graphics... => 0
[[[.,[.,.]],.],[.,[[.,.],.]]] generating graphics... => 0
[[[.,[.,.]],.],[[.,.],[.,.]]] generating graphics... => 0
[[[.,[.,.]],.],[[.,[.,.]],.]] generating graphics... => 0
[[[.,[.,.]],.],[[[.,.],.],.]] generating graphics... => 0
[[[[.,.],.],.],[.,[.,[.,.]]]] generating graphics... => 0
[[[[.,.],.],.],[.,[[.,.],.]]] generating graphics... => 0
[[[[.,.],.],.],[[.,.],[.,.]]] generating graphics... => 0
[[[[.,.],.],.],[[.,[.,.]],.]] generating graphics... => 0
[[[[.,.],.],.],[[[.,.],.],.]] generating graphics... => 0
[[.,[.,[.,[.,.]]]],[.,[.,.]]] generating graphics... => 0
[[.,[.,[.,[.,.]]]],[[.,.],.]] generating graphics... => 0
[[.,[.,[[.,.],.]]],[.,[.,.]]] generating graphics... => 0
[[.,[.,[[.,.],.]]],[[.,.],.]] generating graphics... => 0
[[.,[[.,.],[.,.]]],[.,[.,.]]] generating graphics... => 0
[[.,[[.,.],[.,.]]],[[.,.],.]] generating graphics... => 0
[[.,[[.,[.,.]],.]],[.,[.,.]]] generating graphics... => 0
[[.,[[.,[.,.]],.]],[[.,.],.]] generating graphics... => 0
[[.,[[[.,.],.],.]],[.,[.,.]]] generating graphics... => 0
[[.,[[[.,.],.],.]],[[.,.],.]] generating graphics... => 0
[[[.,.],[.,[.,.]]],[.,[.,.]]] generating graphics... => 0
[[[.,.],[.,[.,.]]],[[.,.],.]] generating graphics... => 0
[[[.,.],[[.,.],.]],[.,[.,.]]] generating graphics... => 0
[[[.,.],[[.,.],.]],[[.,.],.]] generating graphics... => 0
[[[.,[.,.]],[.,.]],[.,[.,.]]] generating graphics... => 0
[[[.,[.,.]],[.,.]],[[.,.],.]] generating graphics... => 0
[[[[.,.],.],[.,.]],[.,[.,.]]] generating graphics... => 0
[[[[.,.],.],[.,.]],[[.,.],.]] generating graphics... => 0
[[[.,[.,[.,.]]],.],[.,[.,.]]] generating graphics... => 0
[[[.,[.,[.,.]]],.],[[.,.],.]] generating graphics... => 0
[[[.,[[.,.],.]],.],[.,[.,.]]] generating graphics... => 0
[[[.,[[.,.],.]],.],[[.,.],.]] generating graphics... => 0
[[[[.,.],[.,.]],.],[.,[.,.]]] generating graphics... => 0
[[[[.,.],[.,.]],.],[[.,.],.]] generating graphics... => 0
[[[[.,[.,.]],.],.],[.,[.,.]]] generating graphics... => 0
[[[[.,[.,.]],.],.],[[.,.],.]] generating graphics... => 0
[[[[[.,.],.],.],.],[.,[.,.]]] generating graphics... => 0
[[[[[.,.],.],.],.],[[.,.],.]] generating graphics... => 0
[[.,[.,[.,[.,[.,.]]]]],[.,.]] generating graphics... => 0
[[.,[.,[.,[[.,.],.]]]],[.,.]] generating graphics... => 0
[[.,[.,[[.,.],[.,.]]]],[.,.]] generating graphics... => 0
[[.,[.,[[.,[.,.]],.]]],[.,.]] generating graphics... => 1
[[.,[.,[[[.,.],.],.]]],[.,.]] generating graphics... => 0
[[.,[[.,.],[.,[.,.]]]],[.,.]] generating graphics... => 0
[[.,[[.,.],[[.,.],.]]],[.,.]] generating graphics... => 0
[[.,[[.,[.,.]],[.,.]]],[.,.]] generating graphics... => 0
[[.,[[[.,.],.],[.,.]]],[.,.]] generating graphics... => 0
[[.,[[.,[.,[.,.]]],.]],[.,.]] generating graphics... => 0
[[.,[[.,[[.,.],.]],.]],[.,.]] generating graphics... => 0
[[.,[[[.,.],[.,.]],.]],[.,.]] generating graphics... => 0
[[.,[[[.,[.,.]],.],.]],[.,.]] generating graphics... => 0
[[.,[[[[.,.],.],.],.]],[.,.]] generating graphics... => 0
[[[.,.],[.,[.,[.,.]]]],[.,.]] generating graphics... => 0
[[[.,.],[.,[[.,.],.]]],[.,.]] generating graphics... => 0
[[[.,.],[[.,.],[.,.]]],[.,.]] generating graphics... => 0
[[[.,.],[[.,[.,.]],.]],[.,.]] generating graphics... => 0
[[[.,.],[[[.,.],.],.]],[.,.]] generating graphics... => 0
[[[.,[.,.]],[.,[.,.]]],[.,.]] generating graphics... => 0
[[[.,[.,.]],[[.,.],.]],[.,.]] generating graphics... => 0
[[[[.,.],.],[.,[.,.]]],[.,.]] generating graphics... => 0
[[[[.,.],.],[[.,.],.]],[.,.]] generating graphics... => 0
[[[.,[.,[.,.]]],[.,.]],[.,.]] generating graphics... => 0
[[[.,[[.,.],.]],[.,.]],[.,.]] generating graphics... => 0
[[[[.,.],[.,.]],[.,.]],[.,.]] generating graphics... => 0
[[[[.,[.,.]],.],[.,.]],[.,.]] generating graphics... => 0
[[[[[.,.],.],.],[.,.]],[.,.]] generating graphics... => 0
[[[.,[.,[.,[.,.]]]],.],[.,.]] generating graphics... => 0
[[[.,[.,[[.,.],.]]],.],[.,.]] generating graphics... => 0
[[[.,[[.,.],[.,.]]],.],[.,.]] generating graphics... => 0
[[[.,[[.,[.,.]],.]],.],[.,.]] generating graphics... => 0
[[[.,[[[.,.],.],.]],.],[.,.]] generating graphics... => 0
[[[[.,.],[.,[.,.]]],.],[.,.]] generating graphics... => 0
[[[[.,.],[[.,.],.]],.],[.,.]] generating graphics... => 0
[[[[.,[.,.]],[.,.]],.],[.,.]] generating graphics... => 0
[[[[[.,.],.],[.,.]],.],[.,.]] generating graphics... => 0
[[[[.,[.,[.,.]]],.],.],[.,.]] generating graphics... => 0
[[[[.,[[.,.],.]],.],.],[.,.]] generating graphics... => 0
[[[[[.,.],[.,.]],.],.],[.,.]] generating graphics... => 0
[[[[[.,[.,.]],.],.],.],[.,.]] generating graphics... => 0
[[[[[[.,.],.],.],.],.],[.,.]] generating graphics... => 0
[[.,[.,[.,[.,[.,[.,.]]]]]],.] generating graphics... => 0
[[.,[.,[.,[.,[[.,.],.]]]]],.] generating graphics... => 0
[[.,[.,[.,[[.,.],[.,.]]]]],.] generating graphics... => 0
[[.,[.,[.,[[.,[.,.]],.]]]],.] generating graphics... => 1
[[.,[.,[.,[[[.,.],.],.]]]],.] generating graphics... => 0
[[.,[.,[[.,.],[.,[.,.]]]]],.] generating graphics... => 0
[[.,[.,[[.,.],[[.,.],.]]]],.] generating graphics... => 0
[[.,[.,[[.,[.,.]],[.,.]]]],.] generating graphics... => 1
[[.,[.,[[[.,.],.],[.,.]]]],.] generating graphics... => 0
[[.,[.,[[.,[.,[.,.]]],.]]],.] generating graphics... => 1
[[.,[.,[[.,[[.,.],.]],.]]],.] generating graphics... => 1
[[.,[.,[[[.,.],[.,.]],.]]],.] generating graphics... => 1
[[.,[.,[[[.,[.,.]],.],.]]],.] generating graphics... => 0
[[.,[.,[[[[.,.],.],.],.]]],.] generating graphics... => 0
[[.,[[.,.],[.,[.,[.,.]]]]],.] generating graphics... => 0
[[.,[[.,.],[.,[[.,.],.]]]],.] generating graphics... => 0
[[.,[[.,.],[[.,.],[.,.]]]],.] generating graphics... => 0
[[.,[[.,.],[[.,[.,.]],.]]],.] generating graphics... => 1
[[.,[[.,.],[[[.,.],.],.]]],.] generating graphics... => 0
[[.,[[.,[.,.]],[.,[.,.]]]],.] generating graphics... => 0
[[.,[[.,[.,.]],[[.,.],.]]],.] generating graphics... => 0
[[.,[[[.,.],.],[.,[.,.]]]],.] generating graphics... => 0
[[.,[[[.,.],.],[[.,.],.]]],.] generating graphics... => 0
[[.,[[.,[.,[.,.]]],[.,.]]],.] generating graphics... => 0
[[.,[[.,[[.,.],.]],[.,.]]],.] generating graphics... => 0
[[.,[[[.,.],[.,.]],[.,.]]],.] generating graphics... => 0
[[.,[[[.,[.,.]],.],[.,.]]],.] generating graphics... => 0
[[.,[[[[.,.],.],.],[.,.]]],.] generating graphics... => 0
[[.,[[.,[.,[.,[.,.]]]],.]],.] generating graphics... => 0
[[.,[[.,[.,[[.,.],.]]],.]],.] generating graphics... => 0
[[.,[[.,[[.,.],[.,.]]],.]],.] generating graphics... => 0
[[.,[[.,[[.,[.,.]],.]],.]],.] generating graphics... => 0
[[.,[[.,[[[.,.],.],.]],.]],.] generating graphics... => 0
[[.,[[[.,.],[.,[.,.]]],.]],.] generating graphics... => 0
[[.,[[[.,.],[[.,.],.]],.]],.] generating graphics... => 0
[[.,[[[.,[.,.]],[.,.]],.]],.] generating graphics... => 0
[[.,[[[[.,.],.],[.,.]],.]],.] generating graphics... => 0
[[.,[[[.,[.,[.,.]]],.],.]],.] generating graphics... => 0
[[.,[[[.,[[.,.],.]],.],.]],.] generating graphics... => 0
[[.,[[[[.,.],[.,.]],.],.]],.] generating graphics... => 0
[[.,[[[[.,[.,.]],.],.],.]],.] generating graphics... => 0
[[.,[[[[[.,.],.],.],.],.]],.] generating graphics... => 0
[[[.,.],[.,[.,[.,[.,.]]]]],.] generating graphics... => 0
[[[.,.],[.,[.,[[.,.],.]]]],.] generating graphics... => 0
[[[.,.],[.,[[.,.],[.,.]]]],.] generating graphics... => 0
[[[.,.],[.,[[.,[.,.]],.]]],.] generating graphics... => 1
[[[.,.],[.,[[[.,.],.],.]]],.] generating graphics... => 0
[[[.,.],[[.,.],[.,[.,.]]]],.] generating graphics... => 0
[[[.,.],[[.,.],[[.,.],.]]],.] generating graphics... => 0
[[[.,.],[[.,[.,.]],[.,.]]],.] generating graphics... => 0
[[[.,.],[[[.,.],.],[.,.]]],.] generating graphics... => 0
[[[.,.],[[.,[.,[.,.]]],.]],.] generating graphics... => 0
[[[.,.],[[.,[[.,.],.]],.]],.] generating graphics... => 0
[[[.,.],[[[.,.],[.,.]],.]],.] generating graphics... => 0
[[[.,.],[[[.,[.,.]],.],.]],.] generating graphics... => 0
[[[.,.],[[[[.,.],.],.],.]],.] generating graphics... => 0
[[[.,[.,.]],[.,[.,[.,.]]]],.] generating graphics... => 0
[[[.,[.,.]],[.,[[.,.],.]]],.] generating graphics... => 0
[[[.,[.,.]],[[.,.],[.,.]]],.] generating graphics... => 0
[[[.,[.,.]],[[.,[.,.]],.]],.] generating graphics... => 0
[[[.,[.,.]],[[[.,.],.],.]],.] generating graphics... => 0
[[[[.,.],.],[.,[.,[.,.]]]],.] generating graphics... => 0
[[[[.,.],.],[.,[[.,.],.]]],.] generating graphics... => 0
[[[[.,.],.],[[.,.],[.,.]]],.] generating graphics... => 0
[[[[.,.],.],[[.,[.,.]],.]],.] generating graphics... => 0
[[[[.,.],.],[[[.,.],.],.]],.] generating graphics... => 0
[[[.,[.,[.,.]]],[.,[.,.]]],.] generating graphics... => 0
[[[.,[.,[.,.]]],[[.,.],.]],.] generating graphics... => 0
[[[.,[[.,.],.]],[.,[.,.]]],.] generating graphics... => 0
[[[.,[[.,.],.]],[[.,.],.]],.] generating graphics... => 0
[[[[.,.],[.,.]],[.,[.,.]]],.] generating graphics... => 0
[[[[.,.],[.,.]],[[.,.],.]],.] generating graphics... => 0
[[[[.,[.,.]],.],[.,[.,.]]],.] generating graphics... => 0
[[[[.,[.,.]],.],[[.,.],.]],.] generating graphics... => 0
[[[[[.,.],.],.],[.,[.,.]]],.] generating graphics... => 0
[[[[[.,.],.],.],[[.,.],.]],.] generating graphics... => 0
[[[.,[.,[.,[.,.]]]],[.,.]],.] generating graphics... => 0
[[[.,[.,[[.,.],.]]],[.,.]],.] generating graphics... => 0
[[[.,[[.,.],[.,.]]],[.,.]],.] generating graphics... => 0
[[[.,[[.,[.,.]],.]],[.,.]],.] generating graphics... => 0
[[[.,[[[.,.],.],.]],[.,.]],.] generating graphics... => 0
[[[[.,.],[.,[.,.]]],[.,.]],.] generating graphics... => 0
[[[[.,.],[[.,.],.]],[.,.]],.] generating graphics... => 0
[[[[.,[.,.]],[.,.]],[.,.]],.] generating graphics... => 0
[[[[[.,.],.],[.,.]],[.,.]],.] generating graphics... => 0
[[[[.,[.,[.,.]]],.],[.,.]],.] generating graphics... => 0
[[[[.,[[.,.],.]],.],[.,.]],.] generating graphics... => 0
[[[[[.,.],[.,.]],.],[.,.]],.] generating graphics... => 0
[[[[[.,[.,.]],.],.],[.,.]],.] generating graphics... => 0
[[[[[[.,.],.],.],.],[.,.]],.] generating graphics... => 0
[[[.,[.,[.,[.,[.,.]]]]],.],.] generating graphics... => 0
[[[.,[.,[.,[[.,.],.]]]],.],.] generating graphics... => 0
[[[.,[.,[[.,.],[.,.]]]],.],.] generating graphics... => 0
[[[.,[.,[[.,[.,.]],.]]],.],.] generating graphics... => 1
[[[.,[.,[[[.,.],.],.]]],.],.] generating graphics... => 0
[[[.,[[.,.],[.,[.,.]]]],.],.] generating graphics... => 0
[[[.,[[.,.],[[.,.],.]]],.],.] generating graphics... => 0
[[[.,[[.,[.,.]],[.,.]]],.],.] generating graphics... => 0
[[[.,[[[.,.],.],[.,.]]],.],.] generating graphics... => 0
[[[.,[[.,[.,[.,.]]],.]],.],.] generating graphics... => 0
[[[.,[[.,[[.,.],.]],.]],.],.] generating graphics... => 0
[[[.,[[[.,.],[.,.]],.]],.],.] generating graphics... => 0
[[[.,[[[.,[.,.]],.],.]],.],.] generating graphics... => 0
[[[.,[[[[.,.],.],.],.]],.],.] generating graphics... => 0
[[[[.,.],[.,[.,[.,.]]]],.],.] generating graphics... => 0
[[[[.,.],[.,[[.,.],.]]],.],.] generating graphics... => 0
[[[[.,.],[[.,.],[.,.]]],.],.] generating graphics... => 0
[[[[.,.],[[.,[.,.]],.]],.],.] generating graphics... => 0
[[[[.,.],[[[.,.],.],.]],.],.] generating graphics... => 0
[[[[.,[.,.]],[.,[.,.]]],.],.] generating graphics... => 0
[[[[.,[.,.]],[[.,.],.]],.],.] generating graphics... => 0
[[[[[.,.],.],[.,[.,.]]],.],.] generating graphics... => 0
[[[[[.,.],.],[[.,.],.]],.],.] generating graphics... => 0
[[[[.,[.,[.,.]]],[.,.]],.],.] generating graphics... => 0
[[[[.,[[.,.],.]],[.,.]],.],.] generating graphics... => 0
[[[[[.,.],[.,.]],[.,.]],.],.] generating graphics... => 0
[[[[[.,[.,.]],.],[.,.]],.],.] generating graphics... => 0
[[[[[[.,.],.],.],[.,.]],.],.] generating graphics... => 0
[[[[.,[.,[.,[.,.]]]],.],.],.] generating graphics... => 0
[[[[.,[.,[[.,.],.]]],.],.],.] generating graphics... => 0
[[[[.,[[.,.],[.,.]]],.],.],.] generating graphics... => 0
[[[[.,[[.,[.,.]],.]],.],.],.] generating graphics... => 0
[[[[.,[[[.,.],.],.]],.],.],.] generating graphics... => 0
[[[[[.,.],[.,[.,.]]],.],.],.] generating graphics... => 0
[[[[[.,.],[[.,.],.]],.],.],.] generating graphics... => 0
[[[[[.,[.,.]],[.,.]],.],.],.] generating graphics... => 0
[[[[[[.,.],.],[.,.]],.],.],.] generating graphics... => 0
[[[[[.,[.,[.,.]]],.],.],.],.] generating graphics... => 0
[[[[[.,[[.,.],.]],.],.],.],.] generating graphics... => 0
[[[[[[.,.],[.,.]],.],.],.],.] generating graphics... => 0
[[[[[[.,[.,.]],.],.],.],.],.] generating graphics... => 0
[[[[[[[.,.],.],.],.],.],.],.] generating graphics... => 0
click to show generating function       
Description
The number of occurrences of the contiguous pattern [.,[.,[[.,[.,.]],.]]] in a binary tree.
oeis:A159769 counts binary trees avoiding this pattern.
References
[1] Rowland, E. S. Pattern avoidance in binary trees MathSciNet:2645188 arXiv:0809.0488
Code
(* in Mathematica *)
tree = {{{{}, {}}, {{}, {}}}, {{{}, {}}, {{}, {}}}};
Count[tree, {{___}, {{___}, {{{___}, {{___}, {___}}}, {___}}}}, {0, Infinity}]

Created
Jun 18, 2013 at 18:53 by Eric Rowland
Updated
Oct 17, 2015 at 11:06 by Christian Stump