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

0,2

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).

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

Mathematica

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

Prog

(Magma) [11*Fibonacci(n): n in [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

Crossrefs

Cf. A000045.

Cf. similar sequences listed in A258160.

Sequence in context: A040111 A003887 A138844 * A246554 A218163 A152082

Adjacent sequences: A022342 A022343 A022344 * A022346 A022347 A022348

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Bruno Berselli, May 22 2015

Status

approved