A245904 a(n) is the number of permutations avoiding 231 and 312 realizable on increasing strict binary trees with 2n-1 nodes.

1, 2, 6, 22, 84, 330, 1308, 5210, 20796, 83100, 332232, 1328598, 5313732, 21253620, 85011864, 340042246, 1360158564

Offset

1,2

Comments

The number of permutations avoiding 231 and 312 in the classical sense which can be realized as labels on an increasing strict binary tree with 2n-1 nodes. A strict binary tree is a tree graph where each node has 0 or 2 children. The permutation is found by reading the labels 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.

Links

Table of n, a(n) for n=1..17.

Example

For example, when n=3, the permutations 12543, 12435, 13245, 13254, 12345,and 12354. all avoid 231 and 312 in the classical sense and occur as breadth-first search reading words on an increasing strict binary tree with 5 nodes.
.      1         1         1         1         1         1
.     / \       / \       / \       / \       / \       / \
.    2   5     2   4     3   2     3   2     2   3     2   3
.   / \       / \       / \       / \       / \       / \
.  4   3     3   5     4   5     5   4     4   5     5   4

Crossrefs

A bisection of A002083.

Sequence in context: A200316 A164870 A121686 * A128723 A150244 A151288

Adjacent sequences: A245901 A245902 A245903 * A245905 A245906 A245907

Keyword

nonn,more

Author

Manda Riehl, Aug 05 2014

Extensions

More terms from N. J. A. Sloane, Jul 07 2015

Status

approved