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A094014
Expansion of (1-2*x)/(1-8*x^2).
6
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
OFFSET
0,2
COMMENTS
Second inverse binomial transform of A094013. Third inverse binomial transform of A000129(2n-1).
The unsigned sequence has g.f. (1+2*x)/(1-8*x^2) and abs(a(n)) = 2^(3*n/2)*(1/2 + sqrt(2)/4 + (1/2 - sqrt(2)/4)*(-1)^n).
FORMULA
a(n) = (2*sqrt(2))^n*(1/2 - sqrt(2)/4) + (-2*sqrt(2))^n*(1/2 + sqrt(2)/4).
a(n) = (-2)^n * A016116(n). - R. J. Mathar, Apr 28 2008
Abs(a(n)) = A113836(n+1) - A113836(n) for n > 0. - Reinhard Zumkeller, Feb 22 2010
a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011
a(n) = Sum_{k=0..n} A158020(n,k)*3^k. - Philippe Deléham, Dec 01 2011
E.g.f.: cosh(2*sqrt(2)*x) - (1/sqrt(2))*sinh(2*sqrt(2)*x). - G. C. Greubel, Dec 04 2021
MATHEMATICA
LinearRecurrence[{0, 8}, {1, -2}, 40] (* G. C. Greubel, Dec 04 2021 *)
PROG
(Magma) [n le 2 select (-2)^(n-1) else 8*Self(n-2): n in [1..41]]; // G. C. Greubel, Dec 04 2021
(Sage) [(-2)^n*2^(n//2) for n in (0..40)] # G. C. Greubel, Dec 04 2021
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Apr 21 2004
STATUS
approved