A081077 a(n) = Lucas(4*n+2) + 3, or Lucas(2*n)*Lucas(2*n+2).

6, 21, 126, 846, 5781, 39606, 271446, 1860501, 12752046, 87403806, 599074581, 4106118246, 28143753126, 192900153621, 1322157322206, 9062201101806, 62113250390421, 425730551631126, 2918000611027446, 20000273725560981

Offset: 0

Author

R. K. Guy, Mar 04 2003

Keywords

• nonn
• easy

References

• Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

Crossrefs

Cf. A000032 (Lucas numbers), A081067.

Programs

Maple

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 40 do printf(`%d,`,luc(4*n+2)+3) od: # James Sellers, Mar 05 2003

Mathematica

Table[LucasL[4*n + 2] + 3, {n, 0, 30}] (* Amiram Eldar, Oct 05 2020 *)

PARI

Vec(-3*(2-9*x+2*x^2)/(x-1)/(x^2-7*x+1) + O(x^30)) \\ Michel Marcus, Dec 23 2014

Formula

a(n) = 8a(n-1) - 8a(n-2) + a(n-3).

a(n) = A081067(n)+1. - R. J. Mathar, May 18 2007

G.f.: -3*(2-9*x+2*x^2)/(x-1)/(x^2-7*x+1) = -3/(x-1)+(-3*x+3)/(x^2-7*x+1). - R. J. Mathar, Nov 18 2007

Sum_{n>=0} 1/a(n) = sqrt(5)/10. - Amiram Eldar, Oct 05 2020

Extensions

More terms from James Sellers, Mar 05 2003