A081019 a(n) = Lucas(4n+3) - 1, or Lucas(2n+1)*Lucas(2n+2).

3, 28, 198, 1363, 9348, 64078, 439203, 3010348, 20633238, 141422323, 969323028, 6643838878, 45537549123, 312119004988, 2139295485798, 14662949395603, 100501350283428, 688846502588398, 4721424167835363, 32361122672259148

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).

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 *)
LinearRecurrence[{8, -8, 1}, {3, 28, 198}, 20] (* Harvey P. Dale, Nov 17 2020 *)

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: A285365 A366689 A160872 * A241455 A356975 A278183

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