

A245899


a(n) is the number of permutations avoiding 312 that can be realized on increasing unarybinary trees with n nodes.


3




OFFSET

1,3


COMMENTS

The number of permutations avoiding 312 in the classical sense which can be realized as labels on an increasing unarybinary tree read in the order they appear in a breadthfirst search. (Note that breadthfirst 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 breadthfirst search reading word, but here we count the permutations, not the trees.


LINKS

Table of n, a(n) for n=1..8.
D. Levin, L. Pudwell, M. Riehl, A. Sandberg, Pattern Avoidance on kary Heaps, Slides of Talk, 2014.


EXAMPLE

For example, when n=4, a(n)=3. The permutations 1234, 1243, and 1324 all avoid 312 in the classical sense and occur as breadthfirst search reading words on an increasing unarybinary tree with 4 nodes:
1 1 1
/ \ / \ / \
2 3 2 4 3 2
  
4 3 4


CROSSREFS

A245902 appears to be the oddindexed terms of this sequence.
Cf. A245889 (the number of increasing unarybinary trees whose breadthfirst reading word avoids 312).
Sequence in context: A306844 A213906 A123777 * A246747 A090828 A296416
Adjacent sequences: A245896 A245897 A245898 * A245900 A245901 A245902


KEYWORD

nonn,more


AUTHOR

Manda Riehl, Aug 06 2014


STATUS

approved



