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A245903 Number of permutations of length 2n-1 avoiding 321 that can be realized on increasing binary trees. 3
1, 2, 10, 79, 753 (list; graph; refs; listen; history; text; internal format)



The number of permutations of length 2n-1 avoiding 321 in the classical sense which can be realized as labels on an increasing 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..5.

Manda Riehl, When n=3, the 10 permutations of length 5 that avoid 321 and can be realized on increasing binary trees.

Manda Riehl, Maple file used to calculate the terms.


For n=3, the a(3)= 10 permutations can be read from the sample trees given in the Links section above.


A245903 appears to be the terms of A245900 with odd indices. A245896 is the number of increasing unary-binary trees whose breadth-first reading word avoids 321.

Sequence in context: A098636 A081363 A279908 * A100248 A108486 A152168

Adjacent sequences:  A245900 A245901 A245902 * A245904 A245905 A245906




Manda Riehl, Aug 22 2014



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Last modified January 18 19:43 EST 2020. Contains 331029 sequences. (Running on oeis4.)