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A245889 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 312. 3
1, 1, 3, 8, 29, 110, 469, 2119 (list; graph; refs; listen; history; text; internal format)



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.


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

Manda Riehl, The 8 trees when n = 4.


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


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 * A013309 A058378 A063839

Adjacent sequences:  A245886 A245887 A245888 * A245890 A245891 A245892




Manda Riehl, Aug 18 2014



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Last modified October 25 16:10 EDT 2021. Contains 348255 sequences. (Running on oeis4.)