A245889 - OEIS

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A245889

Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 312.

1, 1, 3, 8, 29, 110, 469, 2119

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OFFSET

1,3

COMMENTS

The number of labeled increasing unary-binary trees with an associated permutation avoiding 312 in the classical sense. The tree's permutation is found by recording the labels in the order in which they appear in a breadth-first search. (Note that a breadth-first search reading word is equivalent to reading the tree labels left to right by levels, starting with the root.)

In some cases, the same breadth-first search reading permutation can be found on differently shaped trees. This sequence gives the number of trees, not the number of permutations.

LINKS

Table of n, a(n) for n=1..8.

Manda Riehl, The 8 trees when n = 4.

EXAMPLE

When n=4, a(n)=8. In the Links above we show the eight labeled increasing trees on four nodes whose permutation avoids 312.

CROSSREFS

A245895 gives the number of binary trees instead of unary-binary trees. A245899 gives the number of permutations which avoid 312 that are breadth-first reading words on labeled increasing unary-binary trees.

Sequence in context: A148875 A338306 A148876 * A350907 A013309 A058378

Adjacent sequences: A245886 A245887 A245888 * A245890 A245891 A245892

KEYWORD

nonn,more

AUTHOR

Manda Riehl, Aug 18 2014

STATUS

approved