A022091 Fibonacci sequence beginning 0, 8.

0, 8, 8, 16, 24, 40, 64, 104, 168, 272, 440, 712, 1152, 1864, 3016, 4880, 7896, 12776, 20672, 33448, 54120, 87568, 141688, 229256, 370944, 600200, 971144, 1571344, 2542488, 4113832, 6656320, 10770152, 17426472, 28196624, 45623096, 73819720, 119442816, 193262536

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) = round( (16phi-8)/5 phi^n) (works for n>4). - Thomas Baruchel, Sep 08 2004

a(n) = 8*F(n) = F(n+4) + F(n) + F(n-4) for n>3, where F=A000045.

G.f.: 8*x/(1-x-x^2). - Philippe Deléham, Nov 20 2008

E.g.f.: 16*exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5). - Stefano Spezia, Nov 09 2025

Mathematica

8*Fibonacci[Range[0, 41]] (* Vladimir Joseph Stephan Orlovsky, Sep 17 2008; modified by G. C. Greubel, Apr 13 2025 *)
LinearRecurrence[{1, 1}, {0, 8}, 40] (* Harvey P. Dale, Jan 19 2018 *)

Prog

(Magma)
A022091:= func< n | 8*Fibonacci(n) >;
[A022091(n): n in [0..40]]; // G. C. Greubel, Apr 13 2025
(SageMath)
def A022091(n): return 8*fibonacci(n)
print([A022091(n) for n in range(41)]) # G. C. Greubel, Apr 13 2025

Crossrefs

Cf. A000032, A000045, A258160.

Sequences of the form m*Fibonacci are listed in A022086.

Sequence in context: A112439 A309461 A245420 * A171188 A145909 A168409

Adjacent sequences: A022088 A022089 A022090 * A022092 A022093 A022094

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved