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

0,2

References

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 15.

Links

Table of n, a(n) for n=0..36.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (1, 1).

Formula

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

a(n) = 9F(n) = F(n+4) + F(n+1) + F(n-2) + F(n-4), n>3.

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

Mathematica

a={}; b=0; c=9; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 4!}]; a (* Vladimir Joseph Stephan Orlovsky, Sep 17 2008 *)

Crossrefs

Cf. A000032.

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