cp's OEIS Frontend

A245896 Number of labeled increasing binary trees on 2n-1 nodes whose breadth-first reading word avoids 321.

%I A245896 #12 Mar 18 2018 15:12:08
%S A245896 1,2,14,165,2639
%N A245896 Number of labeled increasing binary trees on 2n-1 nodes whose breadth-first reading word avoids 321.
%C A245896 The number of labeled increasing binary trees with an associated permutation avoiding 321 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 A245896 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 A245896 Manda Riehl, <a href="/A245896/a245896.png">For n = 3: the 14 labeled trees on 5 nodes whose associated permutation avoids 321.</a>
%e A245896 When n=3, a(n)=14.  In the Links above we show the fourteen labeled increasing binary trees on five nodes whose permutation avoids 321.
%Y A245896 A245890 gives the number of unary-binary trees instead of binary trees.  A245903 gives the number of permutations which avoid 321 that are breadth-first reading words on labeled increasing binary trees.
%K A245896 nonn,more
%O A245896 1,2
%A A245896 _Manda Riehl_, Aug 22 2014