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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 17 2012
STATUS
approved