A022139 Fibonacci sequence beginning 5, 14.

5, 14, 19, 33, 52, 85, 137, 222, 359, 581, 940, 1521, 2461, 3982, 6443, 10425, 16868, 27293, 44161, 71454, 115615, 187069, 302684, 489753, 792437, 1282190, 2074627, 3356817, 5431444, 8788261, 14219705, 23007966, 37227671, 60235637, 97463308, 157698945

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (1,1).

Crossrefs

Cf. A000032, A000045.

Programs

Mathematica

Transpose[NestList[{#[[2]],#[[1]]+#[[2]]}&,{5,14},30]][[1]]  (* Harvey P. Dale, Feb 07 2011 *)
LinearRecurrence[{1,1},{5,14},40](* Harvey P. Dale, Apr 15 2015 *)

Formula

G.f.: (5+9x)/(1-x-x^2). - Philippe Deléham, Nov 20 2008

a(0)=5, a(1)=14, a(n)=a(n-1)+a(n-2). - Harvey P. Dale, Apr 15 2015

a(n) = Fibonacci(n+6) - Lucas(n-2). - Greg Dresden and Tyler Zidlicky, Mar 01 2022