A134489 a(n) = Fibonacci(5*n + 2).

1, 13, 144, 1597, 17711, 196418, 2178309, 24157817, 267914296, 2971215073, 32951280099, 365435296162, 4052739537881, 44945570212853, 498454011879264, 5527939700884757, 61305790721611591, 679891637638612258

Offset: 0

Author

Artur Jasinski, Oct 28 2007

Keywords

• nonn
• easy

Comments

The o.g.f. of {F(m*n + 2)}_{n>=0}, for m = 1, 2, ..., is

G(m,x) = (1 + F(m - 2)*x) / (1 - L(m)*x + (-1)^m*x^2), with F = A000045 and F(-1) = 1, and L = A000032. - Wolfdieter Lang, Feb 06 2023

Links

• Index entries for linear recurrences with constant coefficients, signature (11,1).

Crossrefs

Cf. A000045, A001906, A001519, A033887, A015448, A014445, A033888-A033891, A102312, A099100, A134490-A134495, A103134, A134497-A134504.

Programs

Magma

[Fibonacci(5*n+2): n in [0..50]]; // Vincenzo Librandi, Apr 20 2011

Mathematica

Table[Fibonacci[5n + 2], {n, 0, 30}]
LinearRecurrence[{11,1},{1,13},20] (* Harvey P. Dale, May 05 2022 *)

Formula

From R. J. Mathar, Jul 04 2011: (Start)

G.f.: (-1-2*x) / (-1 + 11*x + x^2).

a(n) = 2*A049666(n) + A049666(n+1). (End)

a(n) = A000045(A016873(n)). - Michel Marcus, Nov 05 2013