A159773 Number of n-leaf binary trees that do not contain ((()())(()((()())()))) as a subtree.

1, 1, 2, 5, 14, 41, 124, 384, 1212, 3885, 12613, 41389, 137055, 457403, 1536935, 5195215, 17654059, 60273846, 206654787, 711236960, 2456296348, 8509633845, 29565682912, 102993430854, 359654460720, 1258739058760, 4414576865348, 15512503485377, 54608086597058

Offset

1,3

Comments

By 'binary tree' we mean a rooted, ordered tree in which each vertex has either 0 or 2 children.

Links

Table of n, a(n) for n=1..29.

CombOS - Combinatorial Object Server, Generate binary trees

Petr Gregor, Torsten Mütze, and Namrata, Combinatorial generation via permutation languages. VI. Binary trees, arXiv:2306.08420 [cs.DM], 2023.

Eric S. Rowland, Pattern avoidance in binary trees, arXiv:0809.0488 [math.CO], 2008-2010.

Eric S. Rowland, Pattern avoidance in binary trees, J. Comb. Theory A 117 (6) (2010) 741-758.

Formula

G.f. f(x) satisfies x^2 f(x)^3 + (-2 x^3 + 2 x^2 + x) f(x)^2 + (x^4 - 3 x^3 - x^2 + 2 x - 1) f(x) + x (x^3 - x + 1) = 0.

Crossrefs

Sequence in context: A159772 A161898 A159770 * A159769 A159771 A159768

Adjacent sequences: A159770 A159771 A159772 * A159774 A159775 A159776

Keyword

nonn

Author

Eric Rowland, Apr 23 2009

Status

approved