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