A022092 Fibonacci sequence beginning 0, 9.

0, 9, 9, 18, 27, 45, 72, 117, 189, 306, 495, 801, 1296, 2097, 3393, 5490, 8883, 14373, 23256, 37629, 60885, 98514, 159399, 257913, 417312, 675225, 1092537, 1767762, 2860299, 4628061, 7488360, 12116421, 19604781, 31721202, 51325983, 83047185, 134373168

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.

Sequences of the form m*Fibonacci listed in A022086.

Programs

Magma

A022092:= func< n | 9*Fibonacci(n) >;
[A022092(n): n in [0..40]]; // G. C. Greubel, Apr 10 2025

Mathematica

9*Fibonacci[Range[0,40]] (* Vladimir Joseph Stephan Orlovsky, Sep 17 2008 *)

SageMath

def A022092(n): return 9*fibonacci(n)
print([A022092(n) for n in range(41)]) # G. C. Greubel, Apr 10 2025

Formula

a(n) = 9*Fibonacci(n).

a(n) = F(n+4) + F(n+1) + F(n-2) + F(n-4), n>3, where F = A000045.

a(n) = round((18*phi-9)/5 phi^n), for n > 4. - Thomas Baruchel, Sep 08 2004

G.f.: 9*x/(1-x-x^2). - Philippe Deléham, Nov 20 2008