This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A117591 #27 Sep 08 2022 08:45:24
%S A117591 1,3,5,10,19,37,72,141,277,546,1079,2137,4240,8425,16761,33378,66523,
%T A117591 132669,264728,528469,1055341,2108098,4212015,8417265,16823584,
%U A117591 33629457,67230257,134414146,268753267,537385141,1074573864,2148829917
%N A117591 a(n) = 2^n + Fibonacci(n).
%C A117591 a(3n) is even if n>0. - _Robert G. Wilson v_, Sep 06 2002
%C A117591 3 divides a(8n+1) and a(8n-1). - _Enrique Pérez Herrero_, Dec 29 2010
%H A117591 Reinhard Zumkeller, <a href="/A117591/b117591.txt">Table of n, a(n) for n = 0..1000</a>
%H A117591 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-2).
%F A117591 G.f. (1-3*x^2)/((1-x-x^2)*(1-2*x)).
%F A117591 a(n) = A000079(n+1) - A099036(n) = A099036(n) + 2 * A000045(n). - _Reinhard Zumkeller_, Aug 15 2013
%t A117591 Table[f=Fibonacci[n];2^n+f,{n,1,40,1}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 23 2008 *)
%t A117591 CoefficientList[Series[(1-3x^2)/((1-x-x^2)(1-2x)), {x,0,35}], x] (* _Vincenzo Librandi_, Nov 02 2014 *)
%o A117591 (Haskell)
%o A117591 a117591 n = a117591_list !! n
%o A117591 a117591_list = zipWith (+) a000079_list a000045_list
%o A117591 -- _Reinhard Zumkeller_, Aug 15 2013
%o A117591 (Magma) [2^n+Fibonacci(n): n in [0..40]]; // _Vincenzo Librandi_, Nov 02 2014
%o A117591 (PARI) a(n)=2^n + fibonacci(n) \\ _Charles R Greathouse IV_, Oct 07 2016
%o A117591 (Sage) [2^n +fibonacci(n) for n in (0..40)] # _G. C. Greubel_, Jul 05 2021
%Y A117591 Cf. A000045, A000079, A001611, A074824, A099036, A212262.
%K A117591 nonn,easy
%O A117591 0,2
%A A117591 _Franklin T. Adams-Watters_, Apr 04 2006