A022369 Fibonacci sequence beginning 2, 14.

2, 14, 16, 30, 46, 76, 122, 198, 320, 518, 838, 1356, 2194, 3550, 5744, 9294, 15038, 24332, 39370, 63702, 103072, 166774, 269846, 436620, 706466, 1143086, 1849552, 2992638, 4842190, 7834828, 12677018

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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. A022097.

Programs

Mathematica

a={};b=2;c=14;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 *)
Transpose[NestList[{Last[#],Total[#]}&,{2,14},40]][[1]]  (* Harvey P. Dale, Apr 13 2011 *)
LinearRecurrence[{1,1},{2,14},40] (* Harvey P. Dale, Oct 05 2019 *)

PARI

for(n=0,50, print1(2*(Fibonacci(n+2) + 5*Fibonacci(n)), ", ")) \\ G. C. Greubel, Aug 27 2017

Formula

G.f.: (2+12*x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = 2*(Fibonacci(n+2) + 5*Fibonacci(n)). - G. C. Greubel, Aug 27 2017

a(n) = 2 * A022097(n). - Alois P. Heinz, Aug 27 2017