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 A083086 #24 Aug 23 2024 23:22:32
%S A083086 1,0,8,-16,96,-320,1408,-5376,22016,-87040,350208,-1396736,5595136,
%T A083086 -22364160,89489408,-357892096,1431699456,-5726535680,22906667008,
%U A083086 -91625619456,366504574976,-1466014105600,5864064811008,-23456242466816,93825003421696,-375299946577920
%N A083086 a(n) = (2^(n+1) + (-4)^n)/3.
%C A083086 Binomial transform of A083085.
%H A083086 Vincenzo Librandi, <a href="/A083086/b083086.txt">Table of n, a(n) for n = 0..1000</a>
%H A083086 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-2,8).
%F A083086 a(n) = (2*2^n + (-4)^n)/3.
%F A083086 G.f.: (1+2*x)/((1+4*x)*(1-2*x)).
%F A083086 E.g.f.: (2*exp(2*x) + exp(-4*x))/3.
%F A083086 a(n) = (-1)^n*A000079(n)*A078008(n). - _Paul Barry_, Feb 12 2004
%F A083086 a(n) = -2*a(n-1) + 8*a(n-2). - _Vincenzo Librandi_, Nov 12 2011
%t A083086 LinearRecurrence[{-2,8}, {1,0}, 41] (* _G. C. Greubel_, Feb 19 2023 *)
%o A083086 (Magma) [(2*2^n+(-4)^n)/3: n in [0..30]]; // _Vincenzo Librandi_, Nov 12 2011
%o A083086 (PARI) a(n)=(2*2^n+(-4)^n)/3 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A083086 (SageMath) [(2^(n+1)+(-4)^n)/3 for n in range(41)] # _G. C. Greubel_, Feb 19 2023
%Y A083086 Cf. A000079, A078008, A083085, A083216.
%K A083086 sign,easy
%O A083086 0,3
%A A083086 _Paul Barry_, Apr 23 2003