A212262 -id:A212262 - cp's OEIS frontend

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

Franklin T. Adams-Watters, Apr 04 2006

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

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

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

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

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

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 *)

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

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

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

A212323 a(n) = 3^n - Fibonacci(n).

Original entry on oeis.org

1, 2, 8, 25, 78, 238, 721, 2174, 6540, 19649, 58994, 177058, 531297, 1594090, 4782592, 14348297, 43045734, 129138566, 387417905, 1162257286, 3486777636, 10460342257, 31381041898, 94143150170, 282429490113, 847288534418, 2541865706936, 7625597288569

Offset: 0

Bruno Berselli, May 09 2012

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-2,-3).

Cf. A000045, A000244, A099036, A212262.

Magma
```
[3^n-Fibonacci(n): n in [0..27]];
```

Table[3^n - Fibonacci[n], {n, 0, 27}]
LinearRecurrence[{4,-2,-3},{1,2,8},30] (* Harvey P. Dale, Dec 08 2023 *)

for(n=0, 27, print1(3^n-fibonacci(n)", "));

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

cp's OEIS Frontend

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

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