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A245888 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 231. 7
1, 1, 3, 9, 36, 155, 752, 3894 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

LINKS

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

Manda Riehl, The 9 trees when n = 4.

EXAMPLE

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

:

CROSSREFS

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: A106435 A276368 A058540 * A295739 A156016 A032314

Adjacent sequences:  A245885 A245886 A245887 * A245889 A245890 A245891

KEYWORD

nonn,more

AUTHOR

Manda Riehl, Aug 18 2014

STATUS

approved

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Last modified April 26 13:09 EDT 2018. Contains 303116 sequences. (Running on oeis4.)