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A081019 a(n) = Lucas(4n+3) - 1, or Lucas(2n+1)*Lucas(2n+2). 1
3, 28, 198, 1363, 9348, 64078, 439203, 3010348, 20633238, 141422323, 969323028, 6643838878, 45537549123, 312119004988, 2139295485798, 14662949395603, 100501350283428, 688846502588398, 4721424167835363, 32361122672259148 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

FORMULA

a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).

a(n) = -1+2*(((7/2)-(3/2)*sqrt(5))^n+((7/2)+(3/2)*sqrt(5))^n)+sqrt(5)*(((7/2)+(3/2)*sqrt(5))^n -((7/2)-(3/2)*sqrt(5))^n). - Paolo P. Lava, Dec 01 2008

G.f.: (3+4*x-2*x^2)/((1-x)*(1-7*x+x^2)). - Colin Barker, Jun 22 2012

MAPLE

with(combinat): luc := proc(n) option remember: if n=0 then RETURN(2) fi: if n=1 then RETURN(1) fi: luc(n-1)+luc(n-2): end: for n from 0 to 25 do printf(`%d, `, luc(4*n+3)-1) od: # James A. Sellers, Mar 03 2003

MATHEMATICA

LucasL[4*Range[0, 30] +3] -1 (* G. C. Greubel, Jul 14 2019 *)

PROG

(PARI) Vec((2*x^2-4*x-3)/((x-1)*(x^2-7*x+1)) + O(x^30)) \\ Michel Marcus, Dec 23 2014

(PARI) vector(30, n, n--; f=fibonacci; f(4*n+4)+f(4*n+2)-1) \\ G. C. Greubel, Jul 14 2019

(MAGMA) [Lucas(4*n+3)-1: n in [0..30]]; // G. C. Greubel, Jul 14 2019

(Sage) [lucas_number2(4*n+3, 1, -1)-1 for n in (0..30)] # G. C. Greubel, Jul 14 2019

(GAP) List([0..30], n-> Lucas(1, -1, 4*n+3)[2] -1); # G. C. Greubel, Jul 14 2019

CROSSREFS

Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).

Sequence in context: A074922 A285365 A160872 * A241455 A278183 A091120

Adjacent sequences:  A081016 A081017 A081018 * A081020 A081021 A081022

KEYWORD

nonn,easy

AUTHOR

R. K. Guy, Mar 01 2003

EXTENSIONS

More terms from James A. Sellers, Mar 03 2003

STATUS

approved

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Last modified September 15 02:19 EDT 2019. Contains 327062 sequences. (Running on oeis4.)