This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365510 #24 Jul 28 2025 10:51:35 %S A365510 1,2,5,14,41,123,376,1168,3678,11716,37688,122261,399533,1314023 %N A365510 Number of n-vertex binary trees that do not contain 0((00)[0(00)]) as a subtree. %C A365510 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 A365510 Number of n-vertex binary trees that do not contain P as a subtree, where P is one of 0((00)[(00)0]), 0((0[0(00)])0), 0((0[(00)0])0), (00)(0[0(00)]), (00)(0[(00)0]). %H A365510 CombOS - Combinatorial Object Server, <a href="http://combos.org/btree">Generate binary trees</a> %H A365510 Michael Dairyko, Lara Pudwell, Samantha Tyner, and Casey Wynn, <a href="http://arxiv.org/abs/1203.0795">Non-contiguous pattern avoidance in binary trees</a>, arXiv:1203.0795 [math.CO], 2012. %H A365510 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 A365510 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 A365510 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 A365510 Toufik Mansour and Mark Shattuck, <a href="https://arxiv.org/abs/2507.17947">On ascent sequences avoiding 021 and a pattern of length four</a>, arXiv:2507.17947 [math.CO], 2025. See p. 11. %H A365510 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 A365510 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 A365510 Cf. A007051 for pattern 0[[00][0[00]]], i.e., same tree shape, but all edges non-contiguous. %Y A365510 Cf. A159768 for pattern 0((00)(0(00))), i.e., same tree shape, but all edges contiguous. %Y A365510 Cf. A365508, A365509. %K A365510 nonn,more %O A365510 1,2 %A A365510 _Torsten Muetze_, Sep 07 2023