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, 217420353

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) = 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

E.g.f.: 18*exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5). - Stefano Spezia, Nov 09 2025

Mathematica

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

Prog

(Magma)
A022092:= func< n | 9*Fibonacci(n) >;
[A022092(n): n in [0..40]]; // G. C. Greubel, Apr 10 2025
(SageMath)
def A022092(n): return 9*fibonacci(n)
print([A022092(n) for n in range(41)]) # G. C. Greubel, Apr 10 2025

Crossrefs

Cf. A000032, A000045.

Sequences of the form m*Fibonacci listed in A022086.

Sequence in context: A309463 A242892 A112440 * A245430 A161365 A214831

Adjacent sequences: A022089 A022090 A022091 * A022093 A022094 A022095

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved