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 A190963 #30 Jan 11 2024 03:30:51
%S A190963 0,1,3,0,-27,-81,0,729,2187,0,-19683,-59049,0,531441,1594323,0,
%T A190963 -14348907,-43046721,0,387420489,1162261467,0,-10460353203,
%U A190963 -31381059609,0,282429536481,847288609443,0,-7625597484987,-22876792454961,0,205891132094649
%N A190963 a(n) = 3*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.
%H A190963 G. C. Greubel, <a href="/A190963/b190963.txt">Table of n, a(n) for n = 0..1000</a>
%H A190963 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-9).
%F A190963 G.f.: x/(1-3*x+9*x^2). - _Philippe Deléham_, Oct 11 2011
%F A190963 From _G. C. Greubel_, Jan 11 2024: (Start)
%F A190963 a(n) = 3^(n-1)*ChebyshevU(n-1, 1/2).
%F A190963 a(n) = 3^(n-1)*A128834(n).
%F A190963 E.g.f.: (2/(3*sqrt(3)))*exp(3*x/2)*sin(3*sqrt(3)*x/2). (End)
%t A190963 LinearRecurrence[{3,-9}, {0,1}, 50]
%o A190963 (PARI) my(x='x+O('x^30)); concat([0], Vec(x/(1-3*x+9*x^2))) \\ _G. C. Greubel_, Jan 25 2018
%o A190963 (Magma) [n le 2 select n-1 else 3*Self(n-1)-9*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 25 2018
%o A190963 (SageMath)
%o A190963 A190963=BinaryRecurrenceSequence(3,-9,0,1)
%o A190963 [A190963(n) for n in range(41)] # _G. C. Greubel_, Jan 11 2024
%Y A190963 Cf. A190958 (index to generalized Fibonacci sequences).
%Y A190963 Cf. A128834.
%K A190963 sign,easy
%O A190963 0,3
%A A190963 _Vladimir Joseph Stephan Orlovsky_, May 24 2011