A245900 - OEIS

A245900

Number of permutations of [n] avoiding 321 that can be realized on increasing unary-binary trees.

1, 1, 2, 4, 10, 27, 79, 239

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OFFSET

1,3

COMMENTS

The number of permutations avoiding 321 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.

LINKS

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

EXAMPLE

For example, when n=4, a(n)=4. The permutations 1234, 1243, 1324, and 1423 all avoid 321 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

CROSSREFS

Cf. A245903 (odd bisection).

A245890 is the number of increasing unary-binary trees whose breadth-first reading word avoids 321.

Sequence in context: A205480 A108523 A157003 * A114507 A148105 A127386

Adjacent sequences: A245897 A245898 A245899 * A245901 A245902 A245903

KEYWORD

nonn,more

AUTHOR

Manda Riehl, Aug 06 2014

STATUS

approved