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A084634
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Binomial transform of 1,1,1,2,2,2,2,.....
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4
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1, 2, 4, 9, 21, 48, 106, 227, 475, 978, 1992, 4029, 8113, 16292, 32662, 65415, 130935, 261990, 524116, 1048385, 2096941, 4194072, 8388354, 16776939, 33554131, 67108538, 134217376, 268435077, 536870505, 1073741388, 2147483182
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Partial sums of A000325.
Sum [i=0..n : 2^i - i] [From Ctibor O. Zizka (c.zizka(AT)email.cz), Oct 15 2010]
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FORMULA
| a(n)=2^(n+1)-(n^2+n+2)/2; a(n)=1+n+n(n-1)/2+2*sum{k=3..n, C(n, k)}.
O.g.f.: (1-3x+3x^2)/[(1-2x)(1-x)^3]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2008
a(n)=5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2008
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PROG
| (Other) sage: [gaussian_binomial(n, 1, 2)-binomial(n, 2) for n in xrange(1, 32)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2009]
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CROSSREFS
| Sequence in context: A091619 A061439 A027711 * A137256 A051164 A182904
Adjacent sequences: A084631 A084632 A084633 * A084635 A084636 A084637
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KEYWORD
| nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jun 06 2003
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