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 A083297 #24 Sep 08 2022 08:45:10
%S A083297 1,2,20,8,464,-736,12608,-42880,388352,-1805824,12932096,-69203968,
%T A083297 448778240,-2558451712,15887581184,-93178003456,567657955328,
%U A083297 -3371587993600,20366966915072,-121652045676544,732111297314816,-4383871690866688,26338414517288960
%N A083297 a(n) = (4*4^n + (-6)^n)/5.
%C A083297 Binomial transform of A083296.
%H A083297 Iain Fox, <a href="/A083297/b083297.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..300 from Vincenzo Librandi)
%H A083297 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-2,24).
%F A083297 a(n) = (4*4^n + (-6)^n)/5.
%F A083297 G.f.: (1+4*x)/((1-4*x)*(1+6*x)).
%F A083297 E.g.f.: (4*exp(4*x) + exp(-6*x))/5.
%F A083297 a(n) = -2*a(n-1) + 24*a(n-2). - _Iain Fox_, Oct 31 2018
%p A083297 seq(coeff(series((1+4*x)/((1-4*x)*(1+6*x)),x,n+1), x, n), n = 0 .. 25); # _Muniru A Asiru_, Oct 31 2018
%t A083297 CoefficientList[Series[(1 + 4 x)/((1 - 4 x) (1 + 6 x)), {x, 0, 22}], x] (* _Michael De Vlieger_, Oct 31 2018 *)
%t A083297 CoefficientList[Series[(4*Exp[4*x] + Exp[-6*x])/5, {x, 0, 50}], x]*Table[k!, {k, 0, 50}] (* _Stefano Spezia_, Nov 01 2018 *)
%t A083297 LinearRecurrence[{-2,24}, {1,2}, 30] (* _G. C. Greubel_, Nov 07 2018 *)
%o A083297 (Magma) [(4*4^n+(-6)^n)/5: n in [0..30]]; // _Vincenzo Librandi_, Jun 08 2011
%o A083297 (PARI) first(n) = Vec((1+4*x)/((1-4*x)*(1+6*x)) + O(x^n)) \\ _Iain Fox_, Oct 31 2018
%o A083297 (PARI) a(n) = (4*4^n + (-6)^n)/5 \\ _Iain Fox_, Oct 31 2018
%o A083297 (GAP) List([0..25],n->(4*4^n+(-6)^n)/5); # _Muniru A Asiru_, Oct 31 2018
%Y A083297 Cf. A083222.
%K A083297 easy,sign
%O A083297 0,2
%A A083297 _Paul Barry_, Apr 24 2003