OFFSET
1,1
REFERENCES
Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1196
Index entries for linear recurrences with constant coefficients, signature (8,-8,1).
FORMULA
a(n) = 8a(n-1) - 8a(n-2) + a(n-3).
From R. J. Mathar, Sep 03 2010: (Start)
G.f.: x*(-4-12*x+x^2) / ( (x-1)*(x^2-7*x+1)).
a(n) = A056854(n)-3. (End)
From Peter Bala, Nov 30 2013: (Start)
a(n) = Lucas(2*n)^2 - 5.
Sum_{n>=1} 1/a(n) = (5 - sqrt(5))/10. (End)
Sum_{n>=1} 1/a(n) = A244847. - Amiram Eldar, Oct 27 2020
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 1 to 40 do printf(`%d, `, luc(4*n)-3) od: # James A. Sellers, Mar 05 2003
MATHEMATICA
LinearRecurrence[{8, -8, 1}, {4, 44, 319}, 30] (* Harvey P. Dale, Jun 08 2014 *)
Table[LucasL[4*n] - 3, {n, 1, 20}] (* Amiram Eldar, Oct 27 2020 *)
PROG
(PARI) Vec(x*(-4-12*x+x^2) / ( (x-1)*(x^2-7*x+1)) + O(x^30)) \\ Michel Marcus, Dec 23 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Mar 04 2003
STATUS
approved