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*(1-2*x)/((1-x)*(1-7*x+x^2)). - 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 25 do printf(`%d, `, luc(4*n+3)+1) od: # James A. Sellers, Mar 03 2003
MATHEMATICA
LucasL[4*Range[0, 20] +3] +1 (* G. C. Greubel, Jul 14 2019 *)
LinearRecurrence[{8, -8, 1}, {5, 30, 200}, 30] (* Harvey P. Dale, Dec 06 2021 *)
PROG
(PARI) vector(30, n, n--; f=fibonacci; f(4*n+4)+f(4*n+2)+1) \\ G. C. Greubel, Jul 14 2019
(Magma) [Lucas(4*n+3)+1: n in [0..30]]; // G. C. Greubel, Jul 14 2019
(Sage) [lucas_number2(4*n+3, 1, -1)+1 for n in (0..30)] # G. C. Greubel, Jul 14 2019
(GAP) List([0..30], n-> Lucas(1, -1, 4*n+3)[2] +1); # G. C. Greubel, Jul 14 2019
(Python)
from sympy import lucas
def a(n): return lucas(4*n+3) + 1
print([a(n) for n in range(22)]) # Michael S. Branicky, May 30 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Mar 01 2003
EXTENSIONS
More terms from James A. Sellers, Mar 03 2003
STATUS
approved