%I
%S 1,1,3,9,36,155,752,3894
%N Number of labeled increasing unarybinary trees on n nodes whose breadthfirst reading word avoids 231.
%C The number of labeled increasing unarybinary 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 breadthfirst search. (Note that a breadthfirst 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 breadthfirst 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 unarybinary trees.
%Y A245898 gives the number of permutations which avoid 231 that are breadthfirst reading words on labeled increasing unarybinary trees instead of the number of trees.
%K nonn,more
%O 1,3
%A _Manda Riehl_, Aug 18 2014
