A245897 Number of labeled increasing binary trees on 2n-1 nodes whose breadth-first reading word simultaneously avoids 231 and 321.

1, 2, 12, 98, 940

Offset

1,2

Comments

The number of labeled increasing binary trees with an associated permutation simultaneously avoiding 231 and 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.

Links

Table of n, a(n) for n=1..5.

Manda Riehl, For n = 3: the 12 labelled trees on 5 nodes whose associated permutation simultaneously avoids 231 and 321.

Example

When n=3, a(n)=12.  In the Links above we show the twelve labeled increasing binary trees on five nodes whose permutation simultaneously avoids 231 and 321.

Crossrefs

A245893 gives the number of unary-binary trees instead of binary trees. A081294 gives the number of permutations which simultaneously avoid 231 and 321 that are breadth-first reading words on labeled increasing binary trees.

Sequence in context: A308820 A322717 A219538 * A231173 A303203 A372154

Adjacent sequences: A245894 A245895 A245896 * A245898 A245899 A245900

Keyword

nonn,more

Author

Manda Riehl, Aug 22 2014

Status

approved