OFFSET
0,1
REFERENCES
Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
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).
G.f.: 5*(1 -6*x +2*x^2)/((1-x)*(1-7*x+x^2)). - Colin Barker, Jun 22 2012
Sum_{n>=0} 1/a(n) = phi/5, where phi = A001622 = (1 + sqrt(5))/2. - Diego Rattaggi, Apr 22 2020
From G. C. Greubel, May 26 2020: (Start)
a(n) = 5*A064170(n+1).
a(n) = Lucas(n)^4 - 4*(-1)^n*Lucas(n)^2 + 5.
E.g.f.: 3*exp(x) + 2*exp(7*x/2)*cosh(3*sqrt(5)*x/2). (End)
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 30 do printf(`%d, `, luc(4*n)+3) od: # James Sellers, Mar 05 2003
MATHEMATICA
Table[LucasL[4 n] + 3, {n, 0, 30}] (* Wesley Ivan Hurt, Nov 20 2014 *)
PROG
(PARI) Vec(-5*(2*x^2-6*x+1)/((x-1)*(x^2-7*x+1)) + O(x^30)) \\ Michel Marcus, Dec 23 2014
(Magma) [Lucas(4*n) +3: n in [0..30]]; // G. C. Greubel, May 26 2020
(SageMath) [lucas_number2(4*n, 1, -1) + 3 for n in (0..30)] # G. C. Greubel, May 26 2020
(GAP) List([0..30], n-> Lucas(1, -1, 4*n)[2] +3 ); # G. C. Greubel, May 26 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Mar 04 2003
EXTENSIONS
More terms from James Sellers, Mar 05 2003
STATUS
approved