A022352 Fibonacci sequence beginning 0, 18.

0, 18, 18, 36, 54, 90, 144, 234, 378, 612, 990, 1602, 2592, 4194, 6786, 10980, 17766, 28746, 46512, 75258, 121770, 197028, 318798, 515826, 834624, 1350450, 2185074, 3535524, 5720598, 9256122, 14976720

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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. A258160.

Cf. sequences with formula Fibonacci(n+k)+Fibonacci(n-k) listed in A280154.

Programs

Mathematica

a={};b=0;c=18;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 *)
LinearRecurrence[{1,1},{0,18},40] (* or *) Table[9(LucasL[n]- Fibonacci[n]),{n,40}] (* Harvey P. Dale, Oct 09 2013 *)

PARI

for(n=0,50, print1(18*fibonacci(n), ", ")) \\ G. C. Greubel, Aug 26 2017

Formula

G.f.: 18*x/(1-x-x^2). - Philippe Deléham, Nov 20 2008

a(n) = 9*(Lucas(n) - Fibonacci(n)). - Harvey P. Dale, Oct 09 2013