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
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).
Programs
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Mathematica
Table[LucasL[n]*LucasL[n + 1], {n, 0, 33}] (* Amiram Eldar, Oct 06 2020 *) -
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
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PARI
Vec((2-x+2*x^2)/((1+x)*(x^2-3*x+1)) + O(x^30)) \\ Colin Barker, Oct 01 2016
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