edit this statistic or download as text // json
Identifier
Values
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>>> Load all 625 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => 0
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[[.,.],[.,[.,[.,[.,.]]]]] => 2
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[[.,.],[[.,[.,[.,.]]],.]] => 0
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[[.,.],[[[.,[.,.]],.],.]] => 0
[[.,.],[[[[.,.],.],.],.]] => 0
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[[[.,.],.],[.,[.,[.,.]]]] => 1
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[[.,[.,[.,[.,[.,.]]]]],.] => 2
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[.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
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[.,[[.,[.,[.,[.,[.,.]]]]],.]] => 2
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[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 3
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 1
[[.,.],[.,[.,[[[.,.],.],.]]]] => 1
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[.,.],[.,[[.,.],[[.,.],.]]]] => 1
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 1
[[.,.],[.,[[[.,.],.],[.,.]]]] => 1
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[[.,.],[.,[[.,[[.,.],.]],.]]] => 0
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[[.,.],[.,[[[.,[.,.]],.],.]]] => 0
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[[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[.,.],[[.,.],[.,[[.,.],.]]]] => 1
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[[.,.],[[.,.],[[.,[.,.]],.]]] => 0
[[.,.],[[.,.],[[[.,.],.],.]]] => 0
[[.,.],[[.,[.,.]],[.,[.,.]]]] => 1
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[[.,.],[[[.,.],.],[.,[.,.]]]] => 1
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[[.,.],[[.,[.,[.,.]]],[.,.]]] => 0
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[[.,.],[[[[.,.],.],.],[.,.]]] => 0
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 1
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[[.,.],[[.,[[.,[.,.]],.]],.]] => 0
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[[.,.],[[[.,.],[.,[.,.]]],.]] => 0
[[.,.],[[[.,.],[[.,.],.]],.]] => 0
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[[.,.],[[[.,[.,[.,.]]],.],.]] => 0
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[[.,.],[[[[[.,.],.],.],.],.]] => 0
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[[.,[.,.]],[.,[.,[[.,.],.]]]] => 1
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[[.,[.,.]],[.,[[.,[.,.]],.]]] => 0
[[.,[.,.]],[.,[[[.,.],.],.]]] => 0
[[.,[.,.]],[[.,.],[.,[.,.]]]] => 1
[[.,[.,.]],[[.,.],[[.,.],.]]] => 0
[[.,[.,.]],[[.,[.,.]],[.,.]]] => 0
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[[.,[.,.]],[[.,[.,[.,.]]],.]] => 0
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[[.,[.,.]],[[[[.,.],.],.],.]] => 0
[[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
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[[[.,.],.],[.,[[.,[.,.]],.]]] => 0
[[[.,.],.],[.,[[[.,.],.],.]]] => 0
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[[[.,.],.],[[.,.],[[.,.],.]]] => 0
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[[[.,.],.],[[.,[.,[.,.]]],.]] => 0
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[[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[[.,[.,[.,.]]],[.,[[.,.],.]]] => 0
[[.,[.,[.,.]]],[[.,.],[.,.]]] => 0
[[.,[.,[.,.]]],[[.,[.,.]],.]] => 0
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[[.,[[.,.],.]],[[.,.],[.,.]]] => 0
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[[.,[[.,.],.]],[[[.,.],.],.]] => 0
[[[.,.],[.,.]],[.,[.,[.,.]]]] => 1
[[[.,.],[.,.]],[.,[[.,.],.]]] => 0
[[[.,.],[.,.]],[[.,.],[.,.]]] => 0
[[[.,.],[.,.]],[[.,[.,.]],.]] => 0
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[[[.,[.,.]],.],[[.,[.,.]],.]] => 0
[[[.,[.,.]],.],[[[.,.],.],.]] => 0
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[[[[.,.],.],.],[[.,.],[.,.]]] => 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