A081015 a(n) = Lucas(4n+3) + 1, or 5*Fibonacci(2n+1)*Fibonacci(2n+2).

5, 30, 200, 1365, 9350, 64080, 439205, 3010350, 20633240, 141422325, 969323030, 6643838880, 45537549125, 312119004990, 2139295485800, 14662949395605, 100501350283430, 688846502588400, 4721424167835365, 32361122672259150, 221806434537978680, 1520283919093591605

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

Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).

Sequence in context: A034164 A322257 A103433 * A090139 A107265 A196678

Adjacent sequences: A081012 A081013 A081014 * A081016 A081017 A081018

Keyword

nonn,easy

Author

R. K. Guy, Mar 01 2003

Extensions

More terms from James A. Sellers, Mar 03 2003

Status

approved