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A075269
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Product of Lucas numbers and inverted Lucas numbers: a(n)=A000032(n)*A075193(n).
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0
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2, -3, 12, -28, 77, -198, 522, -1363, 3572, -9348, 24477, -64078, 167762, -439203, 1149852, -3010348, 7881197, -20633238, 54018522, -141422323, 370248452, -969323028, 2537720637, -6643838878, 17393796002, -45537549123, 119218851372, -312119004988, 817138163597
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n)=((-1)^n)L(2n+1)+1, L(n)=Lucas numbers.
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FORMULA
| G.f.: (2+x+2x^2)/((1+3x+x^2)(1-x)). a(n)=-3a(n-1)-a(n-2)+5=-2a(n-1)+2a(n-2)+a(n-3)=a(-1-n). - Michael Somos, Apr 07 2003
a(n)=1+(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 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 12 2008
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MATHEMATICA
| CoefficientList[Series[(2 + x + 2x^2)/(1 + 2x - 2x^2 - x^3), {x, 0, 30}], x]
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PROG
| (PARI) a(n)=1+(-1)^n*(fibonacci(n+1)+fibonacci(n-1))
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CROSSREFS
| Cf. A000032, A075193.
Sequence in context: A016021 A173669 A136703 * A089414 A195913 A048085
Adjacent sequences: A075266 A075267 A075268 * A075270 A075271 A075272
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KEYWORD
| easy,sign
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Sep 11 2002
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