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A098149
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a(0)=-1, a(1)=-1, a(n)=-3*a(n-1)-a(n-2) for n>1.
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5
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-1, -1, 4, -11, 29, -76, 199, -521, 1364, -3571, 9349, -24476, 64079, -167761, 439204, -1149851, 3010349, -7881196, 20633239, -54018521, 141422324, -370248451, 969323029, -2537720636, 6643838879, -17393796001, 45537549124, -119218851371
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Sequence relates bisections of Lucas and Fibonacci numbers.
2*a(n) + A098150(n) = 8*(-1)^(n+1)*A001519(n) - (-1)^(n+1)*A005248(n+1). Apparently, if (z(n)) is any sequence of integers (not all zero) satisfying the formula z(n) = 2(z(n-2) - z(n-1)) + z(n-3) then |z(n+1)/z(n)| -> golden ratio phi + 1 = (3+sqrt(5))/2
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| G.f.: -(1+4*x)/(1+3*x+x^2).
a(n) = (-1)^n*A002878(n-1). - R. J. Mathar, Jan 30 2011
-a(n+1) = Sum_{k, 0<=k<=n}(-5)^k*Binomial(n+k,n-k) = Sum_{k, 0<=k<=n}(-5)^k*A085478(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 28 2006
a(n)=-(1/2)*[(-3/2)-(1/2)*sqrt(5)]^n+(1/2)*[(-3/2)-(1/2)*sqrt(5)]^n*sqrt(5)-(1/2)*[(-3/2)+(1/2) *sqrt(5)]^n*sqrt(5)-(1/2)*[(-3/2)+(1/2)*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 19 2008]
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MATHEMATICA
| a[0] = a[1] = -1; a[n_] := a[n] = -3a[n - 2] - a[n - 1]; Table[ a[n], {n, 0, 27}] (from Robert G. Wilson v Sep 01 2004)
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CROSSREFS
| Cf. A098150, A001519, A005248.
Sequence in context: A027968 A027970 A027972 * A002878 A124861 A110579
Adjacent sequences: A098146 A098147 A098148 * A098150 A098151 A098152
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KEYWORD
| easy,sign
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 29 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 1 2004
Simpler definition and generating function from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2006
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