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A348850
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a(n) is the number of labeled rooted unordered binary trees T where the nodes are labeled with distinct positive integers, the root has label n, each parent label equals the sum of its children labels, and T cannot be extended.
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3
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1, 1, 1, 1, 2, 2, 3, 5, 9, 10, 14, 22, 33, 57, 66, 94, 132, 188, 317, 454, 576, 806, 1083, 1535, 2342, 3215, 5231, 5656, 8545, 10804, 15226, 21153, 30342, 44536, 63165, 73877, 107241, 133994, 178497, 247564, 331695, 472331
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OFFSET
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1,5
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COMMENTS
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For any n > 0:
- we can imagine a variant of Grundy's game where we start with n at root position,
- and each move consists in adding to a leaf, say w, two children, u and v such that 0 < u < v and u+v = w and u and v do not already appear in the tree,
- a(n) gives the number of final positions (where no move is possible).
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LINKS
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EXAMPLE
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For n = 1, 2, 3, 4: a(n) = 1:
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1 2 3 4
/ \ / \
1 2 1 3
For n = 5, 6: a(n) = 2:
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5 5 6 6
/ \ / \ / \ / \
1 4 2 3 1 5 2 4
/ \ / \
2 3 1 3
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PROG
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(PARI) See Links section.
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CROSSREFS
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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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