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A245888 Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 231. 7

%I

%S 1,1,3,9,36,155,752,3894

%N Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 231.

%C 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.)

%C 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.

%H Manda Riehl, <a href="/A245888/a245888.png">The 9 trees when n = 4.</a>

%e The a(4) = 9 such trees are:

%e :

%e : 1 1 1 1

%e : /\ /\ /\ /\

%e : 2 3 2 3 3 2 3 2

%e : | | | |

%e : 4 4 4 4

%e :

%e :

%e : 1 1 1 1 1

%e : /\ /\ | | |

%e : 2 4 4 2 2 2 2

%e : | | /\ /\ |

%e : 3 3 3 4 4 3 3

%e : |

%e : 4

%e :

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

%Y 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.

%K nonn,more

%O 1,3

%A _Manda Riehl_, Aug 18 2014

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Last modified August 17 11:05 EDT 2018. Contains 313815 sequences. (Running on oeis4.)