edit this statistic or download as text // json
Identifier
Values
=>
Cc0010;cc-rep
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[[[.,.],.],[[[.,.],[.,.]],.]]=>1 [[[.,.],.],[[[.,[.,.]],.],.]]=>1 [[[.,.],.],[[[[.,.],.],.],.]]=>1 [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>0 [[.,[.,[.,.]]],[.,[[.,.],.]]]=>0 [[.,[.,[.,.]]],[[.,.],[.,.]]]=>0 [[.,[.,[.,.]]],[[.,[.,.]],.]]=>0 [[.,[.,[.,.]]],[[[.,.],.],.]]=>1 [[.,[[.,.],.]],[.,[.,[.,.]]]]=>0 [[.,[[.,.],.]],[.,[[.,.],.]]]=>0 [[.,[[.,.],.]],[[.,.],[.,.]]]=>0 [[.,[[.,.],.]],[[.,[.,.]],.]]=>0 [[.,[[.,.],.]],[[[.,.],.],.]]=>1 [[[.,.],[.,.]],[.,[.,[.,.]]]]=>0 [[[.,.],[.,.]],[.,[[.,.],.]]]=>0 [[[.,.],[.,.]],[[.,.],[.,.]]]=>0 [[[.,.],[.,.]],[[.,[.,.]],.]]=>0 [[[.,.],[.,.]],[[[.,.],.],.]]=>1 [[[.,[.,.]],.],[.,[.,[.,.]]]]=>0 [[[.,[.,.]],.],[.,[[.,.],.]]]=>0 [[[.,[.,.]],.],[[.,.],[.,.]]]=>0 [[[.,[.,.]],.],[[.,[.,.]],.]]=>0 [[[.,[.,.]],.],[[[.,.],.],.]]=>1 [[[[.,.],.],.],[.,[.,[.,.]]]]=>0 [[[[.,.],.],.],[.,[[.,.],.]]]=>0 [[[[.,.],.],.],[[.,.],[.,.]]]=>0 [[[[.,.],.],.],[[.,[.,.]],.]]=>0 [[[[.,.],.],.],[[[.,.],.],.]]=>1 [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>0 [[.,[.,[.,[.,.]]]],[[.,.],.]]=>0 [[.,[.,[[.,.],.]]],[.,[.,.]]]=>0 [[.,[.,[[.,.],.]]],[[.,.],.]]=>0 [[.,[[.,.],[.,.]]],[.,[.,.]]]=>0 [[.,[[.,.],[.,.]]],[[.,.],.]]=>0 [[.,[[.,[.,.]],.]],[.,[.,.]]]=>0 [[.,[[.,[.,.]],.]],[[.,.],.]]=>0 [[.,[[[.,.],.],.]],[.,[.,.]]]=>1 [[.,[[[.,.],.],.]],[[.,.],.]]=>1 [[[.,.],[.,[.,.]]],[.,[.,.]]]=>0 [[[.,.],[.,[.,.]]],[[.,.],.]]=>0 [[[.,.],[[.,.],.]],[.,[.,.]]]=>0 [[[.,.],[[.,.],.]],[[.,.],.]]=>0 [[[.,[.,.]],[.,.]],[.,[.,.]]]=>0 [[[.,[.,.]],[.,.]],[[.,.],.]]=>0 [[[[.,.],.],[.,.]],[.,[.,.]]]=>0 [[[[.,.],.],[.,.]],[[.,.],.]]=>0 [[[.,[.,[.,.]]],.],[.,[.,.]]]=>0 [[[.,[.,[.,.]]],.],[[.,.],.]]=>0 [[[.,[[.,.],.]],.],[.,[.,.]]]=>0 [[[.,[[.,.],.]],.],[[.,.],.]]=>0 [[[[.,.],[.,.]],.],[.,[.,.]]]=>0 [[[[.,.],[.,.]],.],[[.,.],.]]=>0 [[[[.,[.,.]],.],.],[.,[.,.]]]=>0 [[[[.,[.,.]],.],.],[[.,.],.]]=>0 [[[[[.,.],.],.],.],[.,[.,.]]]=>0 [[[[[.,.],.],.],.],[[.,.],.]]=>0 [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>0 [[.,[.,[.,[[.,.],.]]]],[.,.]]=>0 [[.,[.,[[.,.],[.,.]]]],[.,.]]=>0 [[.,[.,[[.,[.,.]],.]]],[.,.]]=>0 [[.,[.,[[[.,.],.],.]]],[.,.]]=>1 [[.,[[.,.],[.,[.,.]]]],[.,.]]=>0 [[.,[[.,.],[[.,.],.]]],[.,.]]=>0 [[.,[[.,[.,.]],[.,.]]],[.,.]]=>0 [[.,[[[.,.],.],[.,.]]],[.,.]]=>1 [[.,[[.,[.,[.,.]]],.]],[.,.]]=>0 [[.,[[.,[[.,.],.]],.]],[.,.]]=>0 [[.,[[[.,.],[.,.]],.]],[.,.]]=>1 [[.,[[[.,[.,.]],.],.]],[.,.]]=>1 [[.,[[[[.,.],.],.],.]],[.,.]]=>1 [[[.,.],[.,[.,[.,.]]]],[.,.]]=>0 [[[.,.],[.,[[.,.],.]]],[.,.]]=>0 [[[.,.],[[.,.],[.,.]]],[.,.]]=>0 [[[.,.],[[.,[.,.]],.]],[.,.]]=>0 [[[.,.],[[[.,.],.],.]],[.,.]]=>1 [[[.,[.,.]],[.,[.,.]]],[.,.]]=>0 [[[.,[.,.]],[[.,.],.]],[.,.]]=>0 [[[[.,.],.],[.,[.,.]]],[.,.]]=>0 [[[[.,.],.],[[.,.],.]],[.,.]]=>0 [[[.,[.,[.,.]]],[.,.]],[.,.]]=>0 [[[.,[[.,.],.]],[.,.]],[.,.]]=>0 [[[[.,.],[.,.]],[.,.]],[.,.]]=>0 [[[[.,[.,.]],.],[.,.]],[.,.]]=>0 [[[[[.,.],.],.],[.,.]],[.,.]]=>0 [[[.,[.,[.,[.,.]]]],.],[.,.]]=>0 [[[.,[.,[[.,.],.]]],.],[.,.]]=>0 [[[.,[[.,.],[.,.]]],.],[.,.]]=>0 [[[.,[[.,[.,.]],.]],.],[.,.]]=>0 [[[.,[[[.,.],.],.]],.],[.,.]]=>1 [[[[.,.],[.,[.,.]]],.],[.,.]]=>0 [[[[.,.],[[.,.],.]],.],[.,.]]=>0 [[[[.,[.,.]],[.,.]],.],[.,.]]=>0 [[[[[.,.],.],[.,.]],.],[.,.]]=>0 [[[[.,[.,[.,.]]],.],.],[.,.]]=>0 [[[[.,[[.,.],.]],.],.],[.,.]]=>0 [[[[[.,.],[.,.]],.],.],[.,.]]=>0 [[[[[.,[.,.]],.],.],.],[.,.]]=>0 [[[[[[.,.],.],.],.],.],[.,.]]=>0 [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>0 [[.,[.,[.,[.,[[.,.],.]]]]],.]=>0 [[.,[.,[.,[[.,.],[.,.]]]]],.]=>0 [[.,[.,[.,[[.,[.,.]],.]]]],.]=>0 [[.,[.,[.,[[[.,.],.],.]]]],.]=>1 [[.,[.,[[.,.],[.,[.,.]]]]],.]=>0 [[.,[.,[[.,.],[[.,.],.]]]],.]=>0 [[.,[.,[[.,[.,.]],[.,.]]]],.]=>0 [[.,[.,[[[.,.],.],[.,.]]]],.]=>1 [[.,[.,[[.,[.,[.,.]]],.]]],.]=>0 [[.,[.,[[.,[[.,.],.]],.]]],.]=>0 [[.,[.,[[[.,.],[.,.]],.]]],.]=>1 [[.,[.,[[[.,[.,.]],.],.]]],.]=>1 [[.,[.,[[[[.,.],.],.],.]]],.]=>1 [[.,[[.,.],[.,[.,[.,.]]]]],.]=>0 [[.,[[.,.],[.,[[.,.],.]]]],.]=>0 [[.,[[.,.],[[.,.],[.,.]]]],.]=>0 [[.,[[.,.],[[.,[.,.]],.]]],.]=>0 [[.,[[.,.],[[[.,.],.],.]]],.]=>1 [[.,[[.,[.,.]],[.,[.,.]]]],.]=>0 [[.,[[.,[.,.]],[[.,.],.]]],.]=>0 [[.,[[[.,.],.],[.,[.,.]]]],.]=>1 [[.,[[[.,.],.],[[.,.],.]]],.]=>1 [[.,[[.,[.,[.,.]]],[.,.]]],.]=>0 [[.,[[.,[[.,.],.]],[.,.]]],.]=>0 [[.,[[[.,.],[.,.]],[.,.]]],.]=>1 [[.,[[[.,[.,.]],.],[.,.]]],.]=>1 [[.,[[[[.,.],.],.],[.,.]]],.]=>1 [[.,[[.,[.,[.,[.,.]]]],.]],.]=>0 [[.,[[.,[.,[[.,.],.]]],.]],.]=>0 [[.,[[.,[[.,.],[.,.]]],.]],.]=>0 [[.,[[.,[[.,[.,.]],.]],.]],.]=>0 [[.,[[.,[[[.,.],.],.]],.]],.]=>1 [[.,[[[.,.],[.,[.,.]]],.]],.]=>1 [[.,[[[.,.],[[.,.],.]],.]],.]=>1 [[.,[[[.,[.,.]],[.,.]],.]],.]=>1 [[.,[[[[.,.],.],[.,.]],.]],.]=>1 [[.,[[[.,[.,[.,.]]],.],.]],.]=>1 [[.,[[[.,[[.,.],.]],.],.]],.]=>1 [[.,[[[[.,.],[.,.]],.],.]],.]=>1 [[.,[[[[.,[.,.]],.],.],.]],.]=>1 [[.,[[[[[.,.],.],.],.],.]],.]=>1 [[[.,.],[.,[.,[.,[.,.]]]]],.]=>0 [[[.,.],[.,[.,[[.,.],.]]]],.]=>0 [[[.,.],[.,[[.,.],[.,.]]]],.]=>0 [[[.,.],[.,[[.,[.,.]],.]]],.]=>0 [[[.,.],[.,[[[.,.],.],.]]],.]=>1 [[[.,.],[[.,.],[.,[.,.]]]],.]=>0 [[[.,.],[[.,.],[[.,.],.]]],.]=>0 [[[.,.],[[.,[.,.]],[.,.]]],.]=>0 [[[.,.],[[[.,.],.],[.,.]]],.]=>1 [[[.,.],[[.,[.,[.,.]]],.]],.]=>0 [[[.,.],[[.,[[.,.],.]],.]],.]=>0 [[[.,.],[[[.,.],[.,.]],.]],.]=>1 [[[.,.],[[[.,[.,.]],.],.]],.]=>1 [[[.,.],[[[[.,.],.],.],.]],.]=>1 [[[.,[.,.]],[.,[.,[.,.]]]],.]=>0 [[[.,[.,.]],[.,[[.,.],.]]],.]=>0 [[[.,[.,.]],[[.,.],[.,.]]],.]=>0 [[[.,[.,.]],[[.,[.,.]],.]],.]=>0 [[[.,[.,.]],[[[.,.],.],.]],.]=>1 [[[[.,.],.],[.,[.,[.,.]]]],.]=>0 [[[[.,.],.],[.,[[.,.],.]]],.]=>0 [[[[.,.],.],[[.,.],[.,.]]],.]=>0 [[[[.,.],.],[[.,[.,.]],.]],.]=>0 [[[[.,.],.],[[[.,.],.],.]],.]=>1 [[[.,[.,[.,.]]],[.,[.,.]]],.]=>0 [[[.,[.,[.,.]]],[[.,.],.]],.]=>0 [[[.,[[.,.],.]],[.,[.,.]]],.]=>0 [[[.,[[.,.],.]],[[.,.],.]],.]=>0 [[[[.,.],[.,.]],[.,[.,.]]],.]=>0 [[[[.,.],[.,.]],[[.,.],.]],.]=>0 [[[[.,[.,.]],.],[.,[.,.]]],.]=>0 [[[[.,[.,.]],.],[[.,.],.]],.]=>0 [[[[[.,.],.],.],[.,[.,.]]],.]=>0 [[[[[.,.],.],.],[[.,.],.]],.]=>0 [[[.,[.,[.,[.,.]]]],[.,.]],.]=>0 [[[.,[.,[[.,.],.]]],[.,.]],.]=>0 [[[.,[[.,.],[.,.]]],[.,.]],.]=>0 [[[.,[[.,[.,.]],.]],[.,.]],.]=>0 [[[.,[[[.,.],.],.]],[.,.]],.]=>1 [[[[.,.],[.,[.,.]]],[.,.]],.]=>0 [[[[.,.],[[.,.],.]],[.,.]],.]=>0 [[[[.,[.,.]],[.,.]],[.,.]],.]=>0 [[[[[.,.],.],[.,.]],[.,.]],.]=>0 [[[[.,[.,[.,.]]],.],[.,.]],.]=>0 [[[[.,[[.,.],.]],.],[.,.]],.]=>0 [[[[[.,.],[.,.]],.],[.,.]],.]=>0 [[[[[.,[.,.]],.],.],[.,.]],.]=>0 [[[[[[.,.],.],.],.],[.,.]],.]=>0 [[[.,[.,[.,[.,[.,.]]]]],.],.]=>0 [[[.,[.,[.,[[.,.],.]]]],.],.]=>0 [[[.,[.,[[.,.],[.,.]]]],.],.]=>0 [[[.,[.,[[.,[.,.]],.]]],.],.]=>0 [[[.,[.,[[[.,.],.],.]]],.],.]=>1 [[[.,[[.,.],[.,[.,.]]]],.],.]=>0 [[[.,[[.,.],[[.,.],.]]],.],.]=>0 [[[.,[[.,[.,.]],[.,.]]],.],.]=>0 [[[.,[[[.,.],.],[.,.]]],.],.]=>1 [[[.,[[.,[.,[.,.]]],.]],.],.]=>0 [[[.,[[.,[[.,.],.]],.]],.],.]=>0 [[[.,[[[.,.],[.,.]],.]],.],.]=>1 [[[.,[[[.,[.,.]],.],.]],.],.]=>1 [[[.,[[[[.,.],.],.],.]],.],.]=>1 [[[[.,.],[.,[.,[.,.]]]],.],.]=>0 [[[[.,.],[.,[[.,.],.]]],.],.]=>0 [[[[.,.],[[.,.],[.,.]]],.],.]=>0 [[[[.,.],[[.,[.,.]],.]],.],.]=>0 [[[[.,.],[[[.,.],.],.]],.],.]=>1 [[[[.,[.,.]],[.,[.,.]]],.],.]=>0 [[[[.,[.,.]],[[.,.],.]],.],.]=>0 [[[[[.,.],.],[.,[.,.]]],.],.]=>0 [[[[[.,.],.],[[.,.],.]],.],.]=>0 [[[[.,[.,[.,.]]],[.,.]],.],.]=>0 [[[[.,[[.,.],.]],[.,.]],.],.]=>0 [[[[[.,.],[.,.]],[.,.]],.],.]=>0 [[[[[.,[.,.]],.],[.,.]],.],.]=>0 [[[[[[.,.],.],.],[.,.]],.],.]=>0 [[[[.,[.,[.,[.,.]]]],.],.],.]=>0 [[[[.,[.,[[.,.],.]]],.],.],.]=>0 [[[[.,[[.,.],[.,.]]],.],.],.]=>0 [[[[.,[[.,[.,.]],.]],.],.],.]=>0 [[[[.,[[[.,.],.],.]],.],.],.]=>1 [[[[[.,.],[.,[.,.]]],.],.],.]=>0 [[[[[.,.],[[.,.],.]],.],.],.]=>0 [[[[[.,[.,.]],[.,.]],.],.],.]=>0 [[[[[[.,.],.],[.,.]],.],.],.]=>0 [[[[[.,[.,[.,.]]],.],.],.],.]=>0 [[[[[.,[[.,.],.]],.],.],.],.]=>0 [[[[[[.,.],[.,.]],.],.],.],.]=>0 [[[[[[.,[.,.]],.],.],.],.],.]=>0 [[[[[[[.,.],.],.],.],.],.],.]=>0
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Description
The number of occurrences of the contiguous pattern [.,[[[.,.],.],.]] in a binary tree.
oeis:A005773 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 18:14 by Eric Rowland
Updated
Oct 17, 2015 at 11:06 by Christian Stump