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A245899 a(n) is the number of permutations avoiding 312 that can be realized on increasing unary-binary trees with n nodes. 3
1, 1, 2, 3, 7, 14, 37, 80 (list; graph; refs; listen; history; text; internal format)



The number of permutations avoiding 312 in the classical sense which can be realized as labels on an increasing unary-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.


Table of n, a(n) for n=1..8.

D. Levin, L. Pudwell, M. Riehl, A. Sandberg, Pattern Avoidance on k-ary Heaps, Slides of Talk, 2014.


For example, when n=4, a(n)=3. The permutations 1234, 1243, and 1324 all avoid 312 in the classical sense and occur as breadth-first search reading words on an increasing unary-binary tree with 4 nodes:

       1           1            1

      / \         / \          / \

     2   3       2   4        3   2

     |           |                |

     4           3                4


A245902 appears to be the odd-indexed terms of this sequence.

Cf. A245889 (the number of increasing unary-binary trees whose breadth-first reading word avoids 312).

Sequence in context: A306844 A213906 A123777 * A246747 A090828 A296416

Adjacent sequences:  A245896 A245897 A245898 * A245900 A245901 A245902




Manda Riehl, Aug 06 2014



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Last modified February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)