A083564 a(n) = L(n)*L(2n), where L(n) are the Lucas numbers (A000204).

3, 21, 72, 329, 1353, 5796, 24447, 103729, 439128, 1860621, 7880997, 33385604, 141421803, 599075421, 2537719272, 10749959329, 45537545553, 192900159396, 817138154247, 3461452823129, 14662949371128, 62113250430021

Offset

1,1

Comments

a(n+1)/a(n) -> (phi)^3 = ((1 + sqrt(5))/2)^3 = 4.236067...

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..160

C. Pita, On s-Fibonomials, J. Int. Seq. 14 (2011) # 11.3.7

Index entries for linear recurrences with constant coefficients, signature (3, 6, -3, -1).

Formula

From Benoit Cloitre, Aug 30 2003: (Start)

a(n) = 3*a(n-1) + 6*a(n-2) - 3*a(n-3) - a(n-4);

a(n) = Fibonacci(4*n)/Fibonacci(n) = A000045(4*n)/A000045(n). (End)

a(n) = Lucas(3*n) + (-1)^n*Lucas(n).

From R. J. Mathar, Oct 27 2008: (Start)

G.f.: x*(3+12*x-9*x^2-4*x^3)/((1+x-x^2)*(1-4*x-x^2)).

a(n) = A061084(n+1) + 2*A001077(n). (End)

a(n) = (1+phi)^n + (-phi)^n + (2*phi+1)^n + (3-2*phi)^n, phi = (1+sqrt(5))/2. - Gary Detlefs, Dec 09 2012

Example

a(4) = Lucas(4)*Lucas(8) = 7*47 = 329.

Mathematica

Table[Fibonacci[n*4]/Fibonacci[n], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, May 02 2011 *)

Prog

(Magma) [Lucas(n)*Lucas(2*n): n in [1..25]]; // Vincenzo Librandi, May 03 2011

Crossrefs

Third row of array A028412.

Sequence in context: A145658 A342548 A188667 * A281008 A238193 A054646

Adjacent sequences: A083561 A083562 A083563 * A083565 A083566 A083567

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 12 2003

Status

approved