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Search: id:A115593
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| A115593 |
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Number of forests of rooted trees with total weight n, where a node at height k has weight 2^k (with root considered to be at height 0). |
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1
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| 1, 1, 1, 2, 2, 3, 4, 6, 7, 10, 13, 17, 22, 29, 38, 50, 64, 82, 107, 136, 175, 224, 288, 363, 465, 587, 748, 942, 1196, 1503, 1902, 2385, 3004, 3765, 4729, 5911, 7406, 9246, 11549, 14395, 17941, 22326, 27767, 34501, 42821, 53134, 65828, 81546, 100871
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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The sequence b(2n)=0, b(2n+1)=a(n) is the number of trees of weight n.
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FORMULA
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Euler transform of b(n), where b(2n+1) = a(n), and b(2n) = 0.
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EXAMPLE
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a(3)=2; one forest with 3 single-node trees, and one with a single two-node tree (root node has weight 1, other node has weight 2).
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CROSSREFS
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Cf. A000081.
Sequence in context: A027194 A039883 A024186 this_sequence A094860 A065417 A005860
Adjacent sequences: A115590 A115591 A115592 this_sequence A115594 A115595 A115596
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KEYWORD
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easy,nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 09 2006
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