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

%I A215602 #48 Jan 06 2023 15:10:52
%S A215602 2,3,12,28,77,198,522,1363,3572,9348,24477,64078,167762,439203,
%T A215602 1149852,3010348,7881197,20633238,54018522,141422323,370248452,
%U A215602 969323028,2537720637,6643838878,17393796002,45537549123,119218851372,312119004988,817138163597,2139295485798,5600748293802,14662949395603,38388099893012,100501350283428
%N A215602 a(n) = L(n)*L(n+1), where L = A000032 (Lucas numbers).
%H A215602 Colin Barker, <a href="/A215602/b215602.txt">Table of n, a(n) for n = 0..1000</a>
%H A215602 Ömer Eğecioğlu, Elif Saygı, and Zülfükar Saygı, <a href="https://doi.org/10.22108/TOC.2022.130675.1912">The Mostar and Wiener index of alternate Lucas cubes</a>, Transactions on Combinatorics (2023) Vol. 12, No. 1, 37-46.
%H A215602 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-1).
%F A215602 G.f.: ( 2-x+2*x^2 ) / ( (1+x)*(x^2-3*x+1) ). - _R. J. Mathar_, Aug 21 2012
%F A215602 a(n) = A002878(n)+(-1)^n. - _R. J. Mathar_, Aug 21 2012
%F A215602 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
%F A215602 a(n) = F(2*n) + F(2*n+2) + (-1)^n with F(k)=A000045(k). - _J. M. Bergot_, Apr 15 2016
%F A215602 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
%F A215602 Sum_{n>=0} (-1)^n/a(n) = sqrt(5)/10. - _Amiram Eldar_, Oct 06 2020
%t A215602 Table[LucasL[n]*LucasL[n + 1], {n, 0, 33}] (* _Amiram Eldar_, Oct 06 2020 *)
%o A215602 (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
%o A215602 (PARI) Vec((2-x+2*x^2)/((1+x)*(x^2-3*x+1)) + O(x^30)) \\ _Colin Barker_, Oct 01 2016
%Y A215602 Cf. A000032, A215580. A075269 is a signed version.
%K A215602 nonn,easy
%O A215602 0,1
%A A215602 _N. J. A. Sloane_, Aug 17 2012