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A365508
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Number of n-vertex binary trees that do not contain 0[0(0[0(00)])] as a subtree.
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2
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1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140
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OFFSET
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1,2
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COMMENTS
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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 P as a subtree, where P is one of 0[0(0((00)0))], 0[0((00)(00))], 0[0((0(00))0)], 0[(00)(0(00))], 0[(00)((00)0)], 0[(0(00))(00)], 0[((00)0)(00)], 0[(0((00)0))0], 0[((00)(00))0], 0[((0(00))0)0], 0(([0(00)]0)0), 0(([(00)0]0)0).
Number of restricted growth strings of set partitions of {1,...,n} that avoid the two patterns 1212 and p, where p is one of 12232, 12113, 12322, 11213.
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LINKS
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CROSSREFS
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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.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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