A022345 Fibonacci sequence beginning 0, 11.

0, 11, 11, 22, 33, 55, 88, 143, 231, 374, 605, 979, 1584, 2563, 4147, 6710, 10857, 17567, 28424, 45991, 74415, 120406, 194821, 315227, 510048, 825275, 1335323, 2160598, 3495921, 5656519, 9152440, 14808959, 23961399, 38770358, 62731757, 101502115, 164233872

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 15.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (1, 1).

Crossrefs

Cf. A000045.

Cf. similar sequences listed in A258160.

Programs

Magma

[11*Fibonacci(n): n in [0..40]]; // Bruno Berselli, May 22 2015

Mathematica

Table[11 Fibonacci(n), {n, 0, 40}] (* Bruno Berselli, May 22 2015 *)

PARI

x='x+O('x^50); concat([0], Vec(11*x/(1-x-x^2))) \\ G. C. Greubel, Aug 25 2017

Formula

a(n) = 11*F(n) = F(n+4) + F(n+2) + F(n) + F(n-2) + F(n-4) with n > 3 and F = A000045.

G.f.: 11*x/(1-x-x^2). - Philippe Deléham, Nov 20 2008

a(n) = Fibonacci(n+5) - Fibonacci(n-5), where Fibonacci(-5..-1) = 5, -3, 2, -1, 1. - Bruno Berselli, May 22 2015

Extensions

More terms from Bruno Berselli, May 22 2015