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A086344
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a(n)=-2*a(n-1)+4*a(n-2), a(0)=1,a(1)=0.
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1
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1, 0, 4, -8, 32, -96, 320, -1024, 3328, -10752, 34816, -112640, 364544, -1179648, 3817472, -12353536, 39976960, -129368064, 418643968, -1354760192, 4384096256, -14187233280, 45910851584, -148570636288, 480784678912, -1555851902976, 5034842521600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Inverse binomial transform of (1,1,5,5,25,25,.....).
The absolute values are the constant terms of the reduction by x^2->x+1 of the polynomial p(n,x) given for d=sqrt(x+1) by p(n,x)=((x+d)^n-(x-d)^n)/(2d), for n>=1. The coefficient of x under this reduction is given by A103435. See A192232 for a discussion of reduction. [From Clark Kimberling, Jun 29 2011]
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FORMULA
| G.f.: (1+2*x)/((1+(1+sqrt(5))*x)(1+(1-sqrt(5))*x)).
E.g.f.: exp(-x)*(cosh(sqrt(5)*x)+sinh(sqrt(5)*x)/sqrt(5)).
a(n)=(sqrt(5)-1)^n*(sqrt(5)/10+1/2)+(-sqrt(5)-1)^n*(1/2-sqrt(5)/10).
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CROSSREFS
| Sequence in context: A094867 A149093 A149094 * A068205 A113479 A103970
Adjacent sequences: A086341 A086342 A086343 * A086345 A086346 A086347
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 17 2003
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