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

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. A000032, A000045, A258160.

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

Programs

Magma

A022091:= func< n | 8*Fibonacci(n) >;
[A022091(n): n in [0..40]]; // G. C. Greubel, Apr 13 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 *)

SageMath

def A022091(n): return 8*fibonacci(n)
print([A022091(n) for n in range(41)]) # G. C. Greubel, Apr 13 2025

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