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Identifier

St000122: Binary trees ⟶ ℤ

Values

[.,.] => 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

[.,[.,[.,[.,[.,[.,.]]]]]] => 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

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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