A245901 -id:A245901 - cp's OEIS frontend

A245898 Number of permutations avoiding 231 that can be realized on increasing unary-binary trees with n nodes.

1, 1, 2, 4, 10, 26, 74, 217

Offset: 1

Manda Riehl, Aug 05 2014

The number of permutations avoiding 231 in the classical sense which can be realized as labels on an increasing unary-binary tree with n nodes 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.

			For example, when n=4, the permutations 1234, 1243, 1324, and 1423 all avoid 231 in the classical sense and occur as breadth-first search reading words on an increasing unary-binary tree with 4 nodes:
       1           1           1           1
      / \         / \         / \         / \
     2   3       2   4       3   2       4   2
     |           |           |               |
     4           3           4               3

A245901 is the terms of A245898 with odd indices. A245888 is the number of increasing unary-binary trees whose breadth-first reading word avoids 231.

A245894 Number of labeled increasing binary trees on 2n-1 nodes whose breadth-first reading word avoids 231.

Original entry on oeis.org

1, 2, 14, 163, 2558

Offset: 1

Manda Riehl, Aug 22 2014

The number of labeled increasing binary trees with an associated permutation avoiding 231 in the classical sense. The tree’s permutation is found by recording the labels in the order 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.

			When n=3, a(n)=14.  In the Links above we show the fourteen labeled increasing binary trees on five nodes whose permutation avoids 231.

Manda Riehl, For n = 3: the 14 labeled trees on 5 nodes whose associated permutation avoids 231.

A245888 gives the number of unary-binary trees instead of binary trees.

A245901 gives the number of permutations which avoid 231 that are breadth-first reading words on labeled increasing binary trees.

cp's OEIS Frontend

A245898 Number of permutations avoiding 231 that can be realized on increasing unary-binary trees with n nodes.

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