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Number of permutations of [n] avoiding 321 that can be realized on increasing unary-binary trees.
2

%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