A022114 Fibonacci sequence beginning 2 9.

2, 9, 11, 20, 31, 51, 82, 133, 215, 348, 563, 911, 1474, 2385, 3859, 6244, 10103, 16347, 26450, 42797, 69247, 112044, 181291, 293335, 474626, 767961, 1242587, 2010548, 3253135, 5263683, 8516818, 13780501, 22297319, 36077820, 58375139, 94452959, 152828098

Offset: 0

Author

N. J. A. Sloane, Jun 14 1998

Keywords

• nonn
• easy

Links

• Ivan Panchenko, 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. A000032, A000045.

Programs

Magma

a0:=2; a1:=9; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]]; // Bruno Berselli, Feb 12 2013

Mathematica

LinearRecurrence[{1,1},{2,9},40] (* Harvey P. Dale, Jul 16 2012 *)
CoefficientList[Series[(2 + 7 x)/(1 - x - x^2), {x, 0, 40}], x] (* Wesley Ivan Hurt, Jun 15 2014 *)

Formula

G.f.: (2+7*x)/(1-x-x^2). - Wesley Ivan Hurt, Jun 15 2014

a(n) = 10*F(n) + F(n-3). - J. M. Bergot, Jul 17 2017

a(n) = Fibonacci(n+5) - Lucas(n-2). - Greg Dresden and Christina Savory, Mar 01 2022