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%I #24 Dec 08 2023 12:29:41
%S 1,2,5,14,41,124,383,1202,3819,12255,39651,129190,423469,1395425
%N Number of n-vertex binary trees that do not contain 0(0[0(0(00))]) as a subtree.
%C By 'binary tree' we mean a rooted, ordered tree which is either empty, denoted by 0, or it has both a left subtree L and a right subtree R (which can be empty), and then it is denoted by (LR) if it is attached by a contiguous edge to its parent, [LR] if attached by a non-contiguous edge, or LR if it is does not have a parent, i.e., if is the root. A contiguous edge in the pattern tree corresponds to a parent-child relation in the host tree (as in Rowland's paper), whereas a non-contiguous edge in the pattern tree corresponds to an ancestor-descendant relation in the host tree (as in the paper by Dairyko, Pudwell, Tyner, and Wynn).
%C Number of n-vertex binary trees that do not contain 0(0[((00)0)0]) as a subtree.
%H CombOS - Combinatorial Object Server, <a href="http://combos.org/btree">Generate binary trees</a>
%H Michael Dairyko, Lara Pudwell, Samantha Tyner, and Casey Wynn, <a href="https://arxiv.org/abs/1203.0795">Non-contiguous pattern avoidance in binary trees</a>, arXiv:1203.0795 [math.CO], 2012.
%H Michael Dairyko, Lara Pudwell, Samantha Tyner, and Casey Wynn, <a href="https://doi.org/10.37236/2099">Non-contiguous pattern avoidance in binary trees</a>, Electron. J. Combin. 19 (2012), no. 3, Paper 22, 21 pp. MR2967227.
%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 Petr Gregor, Torsten Mütze, and Namrata, <a href="https://doi.org/10.4230/LIPIcs.ISAAC.2023.33">Pattern-Avoiding Binary Trees-Generation, Counting, and Bijections</a>, Leibniz Int'l Proc. Informatics (LIPIcs), 34th Int'l Symp. Algor. Comp. (ISAAC 2023). See pp. 33.12, 33.13.
%H Eric S. Rowland, <a href="https://arxiv.org/abs/0809.0488">Pattern avoidance in binary trees</a>, arXiv:0809.0488 [math.CO], 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.
%Y Cf. A007051 for pattern 0[0[0[0[00]]]], i.e., same tree shape, but all edges non-contiguous.
%Y Cf. A036766 for pattern 0(0(0(0(00)))), i.e., same tree shape, but all edges contiguous.
%Y Cf. A365508, A365510.
%K nonn,more
%O 1,2
%A _Torsten Muetze_, Sep 07 2023