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A094014
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Expansion of (1-2x)/(1-8x^2).
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3
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1, -2, 8, -16, 64, -128, 512, -1024, 4096, -8192, 32768, -65536, 262144, -524288, 2097152, -4194304, 16777216, -33554432, 134217728, -268435456, 1073741824, -2147483648, 8589934592, -17179869184, 68719476736, -137438953472
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Second inverse binomial transform of A094013. Third inverse binomial transform of A000129(2n-1). The unsigned sequence has G.f. (1+2x)/(1-8x^2) and a(n)=2^(3n/2)(1/2+sqrt(2)/4+(1/2-sqrt(2)/4)(-1)^n).
ABS(a(n)) = A113836(n+1) - A113836(n) for n>0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 22 2010]
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FORMULA
| a(n)=(2sqrt(2))^n(1/2-sqrt(2)/4)+(-2sqrt(2))^n(1/2+sqrt(2)/4)
a(n)=(-2)^n*A016116(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2008
a(n+3) = a(n+2)*a(n+1)/a(n). [Reinhard Zumkeller, Mar 04 2011]
a(n) = Sum_{k, 0<=k<=n} A158020(n,k)*3^k. - DELEHAM Philippe, Dec 01 2011
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CROSSREFS
| Sequence in context: A026523 A066792 A096195 * A098232 A195798 A100736
Adjacent sequences: A094011 A094012 A094013 * A094015 A094016 A094017
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 21 2004
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