A159770 - OEIS

%I #22 Sep 08 2023 01:20:22

%S 1,1,2,5,14,41,124,384,1211,3875,12548,41040,135370,449791,1504057,

%T 5057668,17092030,58018150,197727023,676290905,2320721255,7987481185,

%U 27566740439,95379299734,330774138321,1149589209136,4003322875481

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

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

%H Alois P. Heinz, <a href="/A159770/b159770.txt">Table of n, a(n) for n = 1..1000</a>

%H CombOS - Combinatorial Object Server, <a href="http://combos.org/btree">Generate binary trees</a>

%H Petr Gregor, Torsten Mütze, and Namrata, <a href="https://arxiv.org/abs/2306.08420">Combinatorial generation via permutation languages. VI. Binary trees</a>, arXiv:2306.08420 [cs.DM], 2023.

%H Eric S. Rowland, <a href="http://arxiv.org/abs/0809.0488">Pattern avoidance in binary trees</a>, arXiv:0809.0488 [math.CO], 2008-2010.

%H Eric S. Rowland, <a href="https://doi.org/10.1016/j.jcta.2010.03.004">Pattern avoidance in binary trees</a>, J. Comb. Theory A 117 (6) (2010) 741-758.

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

%K nonn

%O 1,3

%A _Eric Rowland_, Apr 23 2009