login
Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 321.
3

%I #10 Mar 18 2018 17:32:20

%S 1,1,3,9,37,165,834,4515

%N Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 321.

%C The number of labeled increasing unary-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 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="/A245890/a245890.png">The 9 trees when n=4.</a>

%e When n=4, a(n)=9. In the Links above we show the nine labeled increasing trees on four nodes whose permutation avoids 321.

%Y A245896 gives the number of binary trees instead of unary-binary trees. A245900 gives the number of permutations which avoid 321 that are breadth-first reading words on labeled increasing unary-binary trees.

%K nonn,more

%O 1,3

%A _Manda Riehl_, Aug 19 2014