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A245888
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Number of labeled increasing unary-binary trees on n nodes whose breadth-first reading word avoids 231.
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7
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OFFSET
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1,3
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COMMENTS
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The number of labeled increasing unary-binary 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 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.)
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.
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LINKS
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EXAMPLE
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The a(4) = 9 such trees are:
:
: 1 1 1 1
: /\ /\ /\ /\
: 2 3 2 3 3 2 3 2
: | | | |
: 4 4 4 4
:
:
: 1 1 1 1 1
: /\ /\ | | |
: 2 4 4 2 2 2 2
: | | /\ /\ |
: 3 3 3 4 4 3 3
: |
: 4
:
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CROSSREFS
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A245894 gives the number of such binary trees instead of unary-binary trees.
A245898 gives the number of permutations which avoid 231 that are breadth-first reading words on labeled increasing unary-binary trees instead of the number of trees.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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