1,3

The number of labeled increasing unary-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 in which 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.

Manda Riehl, The 9 trees when n = 4.

The a(4) = 9 such trees are:

:

: 1 1 1 1

: /\ /\ /\ /\

: 2 3 2 3 3 2 3 2

: | | | |

: 4 4 4 4

:

:

: 1 1 1 1 1

: /\ /\ | | |

: 2 4 4 2 2 2 2

: | | /\ /\ |

: 3 3 3 4 4 3 3

: |

: 4

:

A245894 gives the number of such binary trees instead of unary-binary trees.

A245898 gives the number of permutations which avoid 231 that are breadth-first reading words on labeled increasing unary-binary trees instead of the number of trees.

Sequence in context: A276368 A058540 A350451 * A379034 A295739 A156016

Adjacent sequences: A245885 A245886 A245887 * A245889 A245890 A245891

nonn,more

Manda Riehl, Aug 18 2014

approved