A117591 a(n) = 2^n + Fibonacci(n).

1, 3, 5, 10, 19, 37, 72, 141, 277, 546, 1079, 2137, 4240, 8425, 16761, 33378, 66523, 132669, 264728, 528469, 1055341, 2108098, 4212015, 8417265, 16823584, 33629457, 67230257, 134414146, 268753267, 537385141, 1074573864, 2148829917

Offset: 0

Author

Franklin T. Adams-Watters, Apr 04 2006

Keywords

• nonn
• easy

Comments

a(3n) is even if n>0. - Robert G. Wilson v, Sep 06 2002

3 divides a(8n+1) and a(8n-1). - Enrique Pérez Herrero, Dec 29 2010

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).

Crossrefs

Cf. A000045, A000079, A001611, A074824, A099036, A212262.

Programs

Haskell

a117591 n = a117591_list !! n
a117591_list = zipWith (+) a000079_list a000045_list
-- Reinhard Zumkeller, Aug 15 2013

Magma

[2^n+Fibonacci(n): n in [0..40]]; // Vincenzo Librandi, Nov 02 2014

Mathematica

Table[f=Fibonacci[n];2^n+f,{n,1,40,1}] (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
CoefficientList[Series[(1-3x^2)/((1-x-x^2)(1-2x)), {x,0,35}], x] (* Vincenzo Librandi, Nov 02 2014 *)

PARI

a(n)=2^n + fibonacci(n) \\ Charles R Greathouse IV, Oct 07 2016

Sage

[2^n +fibonacci(n) for n in (0..40)] # G. C. Greubel, Jul 05 2021

Formula

G.f. (1-3*x^2)/((1-x-x^2)*(1-2*x)).

a(n) = A000079(n+1) - A099036(n) = A099036(n) + 2 * A000045(n). - Reinhard Zumkeller, Aug 15 2013