A245896 -id:A245896 - cp's OEIS frontend

A245890 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 321.

1, 1, 3, 9, 37, 165, 834, 4515

Offset: 1

Manda Riehl, Aug 19 2014

The number of labeled increasing unary-binary trees with an associated permutation avoiding 321 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)=9.  In the Links above we show the nine labeled increasing trees on four nodes whose permutation avoids 321.

Manda Riehl, The 9 trees when n=4.

A245896 gives the number of binary trees instead of unary-binary trees. A245900 gives the number of permutations which avoid 321 that are breadth-first reading words on labeled increasing unary-binary trees.

A245903 Number of permutations of length 2n-1 avoiding 321 that can be realized on increasing binary trees.

Original entry on oeis.org

1, 2, 10, 79, 753

Offset: 1

Manda Riehl, Aug 22 2014

The number of permutations of length 2n-1 avoiding 321 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)= 10 permutations can be read from the sample trees given in the Links section above.

Manda Riehl, When n=3, the 10 permutations of length 5 that avoid 321 and can be realized on increasing binary trees.
Manda Riehl, Maple file used to calculate the terms.

A245903 appears to be the terms of A245900 with odd indices. A245896 is the number of increasing unary-binary trees whose breadth-first reading word avoids 321.

cp's OEIS Frontend

A245890 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 321.

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