edit this statistic or download as text // json
Identifier
Values
=>
Cc0010;cc-rep
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[[[.,.],.],[[[.,.],[.,.]],.]]=>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 [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>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 [[[[[.,.],.],.],.],[[.,.],.]]=>0 [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>2 [[.,[.,[.,[[.,.],.]]]],[.,.]]=>1 [[.,[.,[[.,.],[.,.]]]],[.,.]]=>1 [[.,[.,[[.,[.,.]],.]]],[.,.]]=>0 [[.,[.,[[[.,.],.],.]]],[.,.]]=>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 [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>3 [[.,[.,[.,[.,[[.,.],.]]]]],.]=>2 [[.,[.,[.,[[.,.],[.,.]]]]],.]=>2 [[.,[.,[.,[[.,[.,.]],.]]]],.]=>1 [[.,[.,[.,[[[.,.],.],.]]]],.]=>1 [[.,[.,[[.,.],[.,[.,.]]]]],.]=>2 [[.,[.,[[.,.],[[.,.],.]]]],.]=>1 [[.,[.,[[.,[.,.]],[.,.]]]],.]=>1 [[.,[.,[[[.,.],.],[.,.]]]],.]=>1 [[.,[.,[[.,[.,[.,.]]],.]]],.]=>0 [[.,[.,[[.,[[.,.],.]],.]]],.]=>0 [[.,[.,[[[.,.],[.,.]],.]]],.]=>0 [[.,[.,[[[.,[.,.]],.],.]]],.]=>0 [[.,[.,[[[[.,.],.],.],.]]],.]=>0 [[.,[[.,.],[.,[.,[.,.]]]]],.]=>2 [[.,[[.,.],[.,[[.,.],.]]]],.]=>1 [[.,[[.,.],[[.,.],[.,.]]]],.]=>1 [[.,[[.,.],[[.,[.,.]],.]]],.]=>0 [[.,[[.,.],[[[.,.],.],.]]],.]=>0 [[.,[[.,[.,.]],[.,[.,.]]]],.]=>1 [[.,[[.,[.,.]],[[.,.],.]]],.]=>0 [[.,[[[.,.],.],[.,[.,.]]]],.]=>1 [[.,[[[.,.],.],[[.,.],.]]],.]=>0 [[.,[[.,[.,[.,.]]],[.,.]]],.]=>0 [[.,[[.,[[.,.],.]],[.,.]]],.]=>0 [[.,[[[.,.],[.,.]],[.,.]]],.]=>0 [[.,[[[.,[.,.]],.],[.,.]]],.]=>0 [[.,[[[[.,.],.],.],[.,.]]],.]=>0 [[.,[[.,[.,[.,[.,.]]]],.]],.]=>1 [[.,[[.,[.,[[.,.],.]]],.]],.]=>0 [[.,[[.,[[.,.],[.,.]]],.]],.]=>0 [[.,[[.,[[.,[.,.]],.]],.]],.]=>0 [[.,[[.,[[[.,.],.],.]],.]],.]=>0 [[.,[[[.,.],[.,[.,.]]],.]],.]=>0 [[.,[[[.,.],[[.,.],.]],.]],.]=>0 [[.,[[[.,[.,.]],[.,.]],.]],.]=>0 [[.,[[[[.,.],.],[.,.]],.]],.]=>0 [[.,[[[.,[.,[.,.]]],.],.]],.]=>0 [[.,[[[.,[[.,.],.]],.],.]],.]=>0 [[.,[[[[.,.],[.,.]],.],.]],.]=>0 [[.,[[[[.,[.,.]],.],.],.]],.]=>0 [[.,[[[[[.,.],.],.],.],.]],.]=>0 [[[.,.],[.,[.,[.,[.,.]]]]],.]=>2 [[[.,.],[.,[.,[[.,.],.]]]],.]=>1 [[[.,.],[.,[[.,.],[.,.]]]],.]=>1 [[[.,.],[.,[[.,[.,.]],.]]],.]=>0 [[[.,.],[.,[[[.,.],.],.]]],.]=>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 [[[.,[.,[.,[.,[.,.]]]]],.],.]=>2 [[[.,[.,[.,[[.,.],.]]]],.],.]=>1 [[[.,[.,[[.,.],[.,.]]]],.],.]=>1 [[[.,[.,[[.,[.,.]],.]]],.],.]=>0 [[[.,[.,[[[.,.],.],.]]],.],.]=>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
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Description
The number of occurrences of the contiguous pattern [.,[.,[.,[.,.]]]] in a binary tree.
oeis:A036765 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 17:47 by Eric Rowland
Updated
Oct 17, 2015 at 11:05 by Christian Stump