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A084636
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Binomial transform of (1,0,1,0,1,0,2,0,2,0,2,0....).
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2
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1, 1, 2, 4, 8, 16, 33, 71, 157, 349, 768, 1662, 3534, 7398, 15291, 31297, 63595, 128555, 258930, 520240, 1043540, 2090956, 4186757, 8379499, 16766313, 33541481, 67093588, 134199826, 268414602, 536846754, 1073713983, 2147451717
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Partial sums are A084637 (without leading 1). The sequence starting 1,2,4,... is the binomial transform of (1,1,1,1,1,2,2,2,....) with a(n)=sum{k=0..4,C(n,k)}+2*sum{k=5..n, C(n,k)}=2^(n+1)-(n^4-2n^3+11n^2+14n+24)/24. This gives the partial sums of A084635.
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FORMULA
| a(n)=sum{k=0..2, C(n, 2k)}+2*sum{k=3..floor(n/2), C(n, 2k)}; a(n)=(n^4-6n^3+23n^2-18n+24)/24+2*sum{k=3..floor(n/2), C(n, 2k)}.
O.g.f.: (2x^2-2x+1)(x^4-2x^3+5x^2-4x+1)/[(-1+x)^5*(-1+2x)]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2008
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CROSSREFS
| Cf. A084634, A000325, A000225.
Sequence in context: A004149 A129986 A110334 * A161869 A088325 A006210
Adjacent sequences: A084633 A084634 A084635 * A084637 A084638 A084639
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jun 06 2003
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