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A075269 Product of Lucas numbers and inverted Lucas numbers: a(n)=A000032(n)*A075193(n). 2
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; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (-2,2,1).

FORMULA

a(n) = 1+(-1)^n*A002878(n).

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, Jun 12 2008

MATHEMATICA

CoefficientList[Series[(2 + x + 2x^2)/(1 + 2x - 2x^2 - x^3), {x, 0, 30}], x]

PROG

(PARI) a(n)=1+(-1)^n*(fibonacci(n+1)+fibonacci(n-1))

CROSSREFS

Cf. A000032, A075193.

Sequence in context: A173669 A136703 A249490 * A215602 A325628 A228501

Adjacent sequences:  A075266 A075267 A075268 * A075270 A075271 A075272

KEYWORD

easy,sign

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Sep 11 2002

STATUS

approved

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Last modified May 16 14:39 EDT 2021. Contains 343949 sequences. (Running on oeis4.)