A245895 -id:A245895 - cp's OEIS frontend

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

Offset: 1

Manda Riehl, Aug 18 2014

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.

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

Manda Riehl, The 8 trees when n = 4.

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.

A245902 Number of permutations of length 2n-1 avoiding 312 that can be realized on increasing binary trees.

Original entry on oeis.org

1, 2, 7, 37, 222

Offset: 1

Manda Riehl, Aug 22 2014

The number of permutations of length 2n-1 avoiding 312 in the classical sense which can be realized as labels on an increasing binary tree read in the order they appear in a breadth-first search. (Note that breadth-first search reading word is equivalent to reading the tree left to right by levels, starting with the root.)

In some cases, more than one tree results in the same breadth-first search reading word, but here we count the permutations, not the trees.

			For n=3, the a(3)= 7 permutations can be read from the sample trees given in the Links section above.

Manda Riehl, When n=3, the 7 permutations of length 5 that avoid 312 and can be realized on increasing binary trees.

A245902 appears to be the terms of A245899 with odd indices. A245895 is the number of increasing unary-binary trees whose breadth-first reading word avoids 312.

cp's OEIS Frontend

A245889 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 312.

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