A215602 a(n) = L(n)*L(n+1), where L = A000032 (Lucas numbers).

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, 2139295485798, 5600748293802, 14662949395603, 38388099893012, 100501350283428

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Ömer Eğecioğlu, Elif Saygı, and Zülfükar Saygı, The Mostar and Wiener index of alternate Lucas cubes, Transactions on Combinatorics (2023) Vol. 12, No. 1, 37-46.

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

Formula

G.f.: ( 2-x+2*x^2 ) / ( (1+x)*(x^2-3*x+1) ). - R. J. Mathar, Aug 21 2012

a(n) = A002878(n)+(-1)^n. - R. J. Mathar, Aug 21 2012

a(n) = F(n-1)*F(n) + F(n-1)*F(n+2) + F(n+1)*F(n) + F(n+1)*F(n+2), where F=A000045, F(-1)=1. - Bruno Berselli, Nov 03 2015

a(n) = F(2*n) + F(2*n+2) + (-1)^n with F(k)=A000045(k). - J. M. Bergot, Apr 15 2016

a(n) = ((-1)^n+(2^(-1-n)*((3-sqrt(5))^n*(-5+sqrt(5))+(3+sqrt(5))^n*(5+sqrt(5)))) / sqrt(5)). - Colin Barker, Oct 01 2016

Sum_{n>=0} (-1)^n/a(n) = sqrt(5)/10. - Amiram Eldar, Oct 06 2020

Mathematica

Table[LucasL[n]*LucasL[n + 1], {n, 0, 33}] (* Amiram Eldar, Oct 06 2020 *)

Prog

(PARI) a(n) = round(((-1)^n+(2^(-1-n)*((3-sqrt(5))^n*(-5+sqrt(5))+(3+sqrt(5))^n*(5+sqrt(5))))/sqrt(5))) \\ Colin Barker, Oct 01 2016
(PARI) Vec((2-x+2*x^2)/((1+x)*(x^2-3*x+1)) + O(x^30)) \\ Colin Barker, Oct 01 2016

Crossrefs

Cf. A000032, A215580. A075269 is a signed version.

Sequence in context: A349016 A249490 A075269 * A325628 A359221 A228501

Adjacent sequences: A215599 A215600 A215601 * A215603 A215604 A215605

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 17 2012

Status

approved