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 A190966 #36 Jan 04 2025 14:01:38
%S A190966 0,1,4,8,0,-64,-256,-512,0,4096,16384,32768,0,-262144,-1048576,
%T A190966 -2097152,0,16777216,67108864,134217728,0,-1073741824,-4294967296,
%U A190966 -8589934592,0,68719476736,274877906944,549755813888,0,-4398046511104,-17592186044416,-35184372088832
%N A190966 a(n) = 4*a(n-1) - 8*a(n-2), with a(0)=0, a(1)=1.
%H A190966 G. C. Greubel, <a href="/A190966/b190966.txt">Table of n, a(n) for n = 0..1000</a>
%H A190966 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-8).
%F A190966 G.f.: x/(1 - 4*x + 8*x^2). - _Philippe Deléham_, Oct 12 2011
%F A190966 a(n) = 2^(n-1)*A009545(n). - _R. J. Mathar_, Apr 07 2022
%F A190966 From _G. C. Greubel_, Jan 10 2024: (Start)
%F A190966 a(n) = 8^((n-1)/2)*ChebyshevU(n-1, 1/sqrt(2)).
%F A190966 E.g.f.: (1/2)*exp(2*x)*sin(2*x). (End)
%F A190966 a(n) = (i/4)*((2 - 2*i)^n - (2 + 2*i)^n), where i=sqrt(-1). - _Taras Goy_, Jan 04 2025
%t A190966 LinearRecurrence[{4,-8}, {0,1}, 50]
%o A190966 (Magma) [n le 2 select n-1 else 4*(Self(n-1) -2*Self(n-2)): n in [1..41]]; // _G. C. Greubel_, Jan 10 2024
%o A190966 (SageMath)
%o A190966 A190966=BinaryRecurrenceSequence(4,-8,0,1)
%o A190966 [A190966(n) for n in range(41)] # _G. C. Greubel_, Jan 10 2024
%Y A190966 Cf. A190958 (index to generalized Fibonacci sequences).
%K A190966 sign,easy
%O A190966 0,3
%A A190966 _Vladimir Joseph Stephan Orlovsky_, May 24 2011