%I #15 Jun 04 2018 14:43:44
%S 1,1,2,4,10,27,79,239
%N Number of permutations of [n] avoiding 321 that can be realized on increasing unary-binary trees.
%C The number of permutations avoiding 321 in the classical sense which can be realized as labels on an increasing unary-binary tree read in the order they appear in a breadth-first search. (Note that breadth-first search reading word is equivalent to reading the tree left to right by levels, starting with the root.)
%C In some cases, more than one tree results in the same breadth-first search reading word, but here we count the permutations, not the trees.
%e For example, when n=4, a(n)=4. The permutations 1234, 1243, 1324, and 1423 all avoid 321 in the classical sense and occur as breadth-first search reading words on an increasing unary-binary tree with 4 nodes:
%e 1 1 1 1
%e / \ / \ / \ / \
%e 2 3 2 4 3 2 4 2
%e | | | |
%e 4 3 4 3
%Y Cf. A245903 (odd bisection).
%Y A245890 is the number of increasing unary-binary trees whose breadth-first reading word avoids 321.
%K nonn,more
%O 1,3
%A _Manda Riehl_, Aug 06 2014