OFFSET
0,2
REFERENCES
Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
LINKS
Hang Gu and Robert M. Ziff, Crossing on hyperbolic lattices, arXiv:1111.5626 [cond-mat.dis-nn], 2011-2012 (see Eq. 4).
Index entries for linear recurrences with constant coefficients, signature (8,-8,1).
FORMULA
a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
a(n) = 5*A049684(n).
G.f.: 5*x*(x+1)/((1-x)*(x^2-7*x+1)). - Colin Barker, Jun 24 2012
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) od: # James A. Sellers, Mar 05 2003
MATHEMATICA
LinearRecurrence[{8, -8, 1}, {0, 5, 45}, 20] (* Jean-François Alcover, Nov 24 2017 *)
PROG
(Magma) [Lucas(4*n)-2: n in [0..30]]; // Vincenzo Librandi, Apr 21 2011
(PARI) a(n) = 5*fibonacci(2*n)^2; \\ Michel Marcus, Nov 24 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Mar 04 2003
STATUS
approved