A022368 Fibonacci sequence beginning 2, 12.

2, 12, 14, 26, 40, 66, 106, 172, 278, 450, 728, 1178, 1906, 3084, 4990, 8074, 13064, 21138, 34202, 55340, 89542, 144882, 234424, 379306, 613730, 993036, 1606766, 2599802, 4206568, 6806370, 11012938

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).

Programs

Mathematica

a={};b=2;c=12;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 18 2008 *)
Table[2*(Fibonacci[n + 2] + 4*Fibonacci[n]), {n,0,50}] (* or *) LinearRecurrence[{1,1}, {2,12}, 50] (* G. C. Greubel, Aug 27 2017 *)

PARI

for(n=0,50, print1(2*(fibonacci(n+2) + 4*fibonacci(n)), ", ")) \\ G. C. Greubel, Aug 27 2017

Formula

G.f.: 2*(1+5*x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = 2*A022096(n). - R. J. Mathar, Sep 27 2014

a(n) = 2*(Fibonacci(n+2) + 4*Fibonacci(n)). - G. C. Greubel, Aug 27 2017