A245892 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word simultaneously avoids 231 and 312 (or avoids 312 and 321).

1, 1, 3, 8, 28, 102, 407, 1701

Offset: 1

Author

Manda Riehl, Aug 19 2014

Keywords

• nonn
• more

Comments

The number of labeled increasing unary-binary trees with an associated permutation avoiding 231 and 312 simultaneously (or avoids 312 and 321 simultaneously) 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.

Examples

			When n=4, a(n)=8.  In the Links above we show the eight labeled increasing trees on four nodes whose permutation simultaneously avoids 231 and 312.
		

Links

• Manda Riehl, The eight trees when n=4.

Crossrefs

A111554 gives the number of binary trees instead of unary-binary trees.

A002083 gives the number of permutations which avoid 231 and 312 simultaneously that are breadth-first reading words on labeled increasing unary-binary trees.