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A084635
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Binomial transform of 1,0,1,0,1,1,1,...
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2
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1, 1, 2, 4, 8, 17, 38, 86, 192, 419, 894, 1872, 3864, 7893, 16006, 32298, 64960, 130375, 261310, 523300, 1047416, 2095801, 4192742, 8386814, 16775168, 33552107, 67106238, 134214776, 268432152, 536867229, 1073737734, 2147479122
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The sequence 1,2,4... has a(n)=2^(n+1)-(n^3+5n+6)/6 =sum{k=0..3,C(n,k)}+2*sum{k=4..n,C(n,k)}. It is the binomial transform of 1,1,1,1,2,2,2,2,2...
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FORMULA
| a(n)=2^n-n(n^2-3n+8)/6; a(n)=1+C(n, 2)+sum{k=4..n, C(n, k)}.
O.g.f.: (-5x+10x^2-10x^3+5x^4+1)/[(-1+x)^4*(1-2x)]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 2008
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CROSSREFS
| Cf. A000325, A084634.
Sequence in context: A179476 A087803 A036374 * A154222 A114199 A006196
Adjacent sequences: A084632 A084633 A084634 * A084636 A084637 A084638
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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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