edit this statistic or download as text // json
Identifier
Values
=>
Cc0010;cc-rep
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[[[.,.],.],[[[.,.],[.,.]],.]]=>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 [[.,[.,[[.,.],.]]],[.,[.,.]]]=>1 [[.,[.,[[.,.],.]]],[[.,.],.]]=>1 [[.,[[.,.],[.,.]]],[.,[.,.]]]=>0 [[.,[[.,.],[.,.]]],[[.,.],.]]=>0 [[.,[[.,[.,.]],.]],[.,[.,.]]]=>0 [[.,[[.,[.,.]],.]],[[.,.],.]]=>0 [[.,[[[.,.],.],.]],[.,[.,.]]]=>0 [[.,[[[.,.],.],.]],[[.,.],.]]=>0 [[[.,.],[.,[.,.]]],[.,[.,.]]]=>0 [[[.,.],[.,[.,.]]],[[.,.],.]]=>0 [[[.,.],[[.,.],.]],[.,[.,.]]]=>0 [[[.,.],[[.,.],.]],[[.,.],.]]=>0 [[[.,[.,.]],[.,.]],[.,[.,.]]]=>0 [[[.,[.,.]],[.,.]],[[.,.],.]]=>0 [[[[.,.],.],[.,.]],[.,[.,.]]]=>0 [[[[.,.],.],[.,.]],[[.,.],.]]=>0 [[[.,[.,[.,.]]],.],[.,[.,.]]]=>0 [[[.,[.,[.,.]]],.],[[.,.],.]]=>0 [[[.,[[.,.],.]],.],[.,[.,.]]]=>0 [[[.,[[.,.],.]],.],[[.,.],.]]=>0 [[[[.,.],[.,.]],.],[.,[.,.]]]=>0 [[[[.,.],[.,.]],.],[[.,.],.]]=>0 [[[[.,[.,.]],.],.],[.,[.,.]]]=>0 [[[[.,[.,.]],.],.],[[.,.],.]]=>0 [[[[[.,.],.],.],.],[.,[.,.]]]=>0 [[[[[.,.],.],.],.],[[.,.],.]]=>0 [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>0 [[.,[.,[.,[[.,.],.]]]],[.,.]]=>1 [[.,[.,[[.,.],[.,.]]]],[.,.]]=>1 [[.,[.,[[.,[.,.]],.]]],[.,.]]=>1 [[.,[.,[[[.,.],.],.]]],[.,.]]=>1 [[.,[[.,.],[.,[.,.]]]],[.,.]]=>0 [[.,[[.,.],[[.,.],.]]],[.,.]]=>1 [[.,[[.,[.,.]],[.,.]]],[.,.]]=>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 [[[[.,.],[.,[.,.]]],.],[.,.]]=>0 [[[[.,.],[[.,.],.]],.],[.,.]]=>0 [[[[.,[.,.]],[.,.]],.],[.,.]]=>0 [[[[[.,.],.],[.,.]],.],[.,.]]=>0 [[[[.,[.,[.,.]]],.],.],[.,.]]=>0 [[[[.,[[.,.],.]],.],.],[.,.]]=>0 [[[[[.,.],[.,.]],.],.],[.,.]]=>0 [[[[[.,[.,.]],.],.],.],[.,.]]=>0 [[[[[[.,.],.],.],.],.],[.,.]]=>0 [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>0 [[.,[.,[.,[.,[[.,.],.]]]]],.]=>1 [[.,[.,[.,[[.,.],[.,.]]]]],.]=>1 [[.,[.,[.,[[.,[.,.]],.]]]],.]=>1 [[.,[.,[.,[[[.,.],.],.]]]],.]=>1 [[.,[.,[[.,.],[.,[.,.]]]]],.]=>1 [[.,[.,[[.,.],[[.,.],.]]]],.]=>2 [[.,[.,[[.,[.,.]],[.,.]]]],.]=>1 [[.,[.,[[[.,.],.],[.,.]]]],.]=>1 [[.,[.,[[.,[.,[.,.]]],.]]],.]=>1 [[.,[.,[[.,[[.,.],.]],.]]],.]=>1 [[.,[.,[[[.,.],[.,.]],.]]],.]=>1 [[.,[.,[[[.,[.,.]],.],.]]],.]=>1 [[.,[.,[[[[.,.],.],.],.]]],.]=>1 [[.,[[.,.],[.,[.,[.,.]]]]],.]=>0 [[.,[[.,.],[.,[[.,.],.]]]],.]=>1 [[.,[[.,.],[[.,.],[.,.]]]],.]=>1 [[.,[[.,.],[[.,[.,.]],.]]],.]=>1 [[.,[[.,.],[[[.,.],.],.]]],.]=>1 [[.,[[.,[.,.]],[.,[.,.]]]],.]=>0 [[.,[[.,[.,.]],[[.,.],.]]],.]=>1 [[.,[[[.,.],.],[.,[.,.]]]],.]=>0 [[.,[[[.,.],.],[[.,.],.]]],.]=>1 [[.,[[.,[.,[.,.]]],[.,.]]],.]=>0 [[.,[[.,[[.,.],.]],[.,.]]],.]=>0 [[.,[[[.,.],[.,.]],[.,.]]],.]=>0 [[.,[[[.,[.,.]],.],[.,.]]],.]=>0 [[.,[[[[.,.],.],.],[.,.]]],.]=>0 [[.,[[.,[.,[.,[.,.]]]],.]],.]=>0 [[.,[[.,[.,[[.,.],.]]],.]],.]=>1 [[.,[[.,[[.,.],[.,.]]],.]],.]=>0 [[.,[[.,[[.,[.,.]],.]],.]],.]=>0 [[.,[[.,[[[.,.],.],.]],.]],.]=>0 [[.,[[[.,.],[.,[.,.]]],.]],.]=>0 [[.,[[[.,.],[[.,.],.]],.]],.]=>0 [[.,[[[.,[.,.]],[.,.]],.]],.]=>0 [[.,[[[[.,.],.],[.,.]],.]],.]=>0 [[.,[[[.,[.,[.,.]]],.],.]],.]=>0 [[.,[[[.,[[.,.],.]],.],.]],.]=>0 [[.,[[[[.,.],[.,.]],.],.]],.]=>0 [[.,[[[[.,[.,.]],.],.],.]],.]=>0 [[.,[[[[[.,.],.],.],.],.]],.]=>0 [[[.,.],[.,[.,[.,[.,.]]]]],.]=>0 [[[.,.],[.,[.,[[.,.],.]]]],.]=>1 [[[.,.],[.,[[.,.],[.,.]]]],.]=>1 [[[.,.],[.,[[.,[.,.]],.]]],.]=>1 [[[.,.],[.,[[[.,.],.],.]]],.]=>1 [[[.,.],[[.,.],[.,[.,.]]]],.]=>0 [[[.,.],[[.,.],[[.,.],.]]],.]=>1 [[[.,.],[[.,[.,.]],[.,.]]],.]=>0 [[[.,.],[[[.,.],.],[.,.]]],.]=>0 [[[.,.],[[.,[.,[.,.]]],.]],.]=>0 [[[.,.],[[.,[[.,.],.]],.]],.]=>0 [[[.,.],[[[.,.],[.,.]],.]],.]=>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 [[[.,[.,[[.,.],[.,.]]]],.],.]=>1 [[[.,[.,[[.,[.,.]],.]]],.],.]=>1 [[[.,[.,[[[.,.],.],.]]],.],.]=>1 [[[.,[[.,.],[.,[.,.]]]],.],.]=>0 [[[.,[[.,.],[[.,.],.]]],.],.]=>1 [[[.,[[.,[.,.]],[.,.]]],.],.]=>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 [[[[[.,.],[.,[.,.]]],.],.],.]=>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:A086581 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 17:54 by Eric Rowland
Updated
Oct 17, 2015 at 11:06 by Christian Stump