A365509 Number of n-vertex binary trees that do not contain 0(0[0(0(00))]) as a subtree.

1, 2, 5, 14, 41, 124, 383, 1202, 3819, 12255, 39651, 129190, 423469, 1395425

Offset

1,2

Comments

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).

Number of n-vertex binary trees that do not contain 0(0[((00)0)0]) as a subtree.

Links

Table of n, a(n) for n=1..14.

CombOS - Combinatorial Object Server, Generate binary trees

Michael Dairyko, Lara Pudwell, Samantha Tyner, and Casey Wynn, Non-contiguous pattern avoidance in binary trees, arXiv:1203.0795 [math.CO], 2012.

Michael Dairyko, Lara Pudwell, Samantha Tyner, and Casey Wynn, Non-contiguous pattern avoidance in binary trees, Electron. J. Combin. 19 (2012), no. 3, Paper 22, 21 pp. MR2967227.

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

Petr Gregor, Torsten Mütze, and Namrata, Pattern-Avoiding Binary Trees-Generation, Counting, and Bijections, Leibniz Int'l Proc. Informatics (LIPIcs), 34th Int'l Symp. Algor. Comp. (ISAAC 2023). See pp. 33.12, 33.13.

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

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

Crossrefs

Cf. A007051 for pattern 0[0[0[0[00]]]], i.e., same tree shape, but all edges non-contiguous.

Cf. A036766 for pattern 0(0(0(0(00)))), i.e., same tree shape, but all edges contiguous.

Cf. A365508, A365510.

Sequence in context: A176677 A365510 A108626 * A366046 A159772 A161898

Adjacent sequences: A365506 A365507 A365508 * A365510 A365511 A365512

Keyword

nonn,more

Author

Torsten Muetze, Sep 07 2023

Status

approved