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 A100219 #21 Apr 28 2024 11:34:13
%S A100219 1,0,-2,-3,-2,0,1,0,-2,-3,-2,0,1,0,-2,-3,-2,0,1,0,-2,-3,-2,0,1,0,-2,
%T A100219 -3,-2,0,1,0,-2,-3,-2,0,1,0,-2,-3,-2,0,1,0,-2,-3,-2,0,1,0,-2,-3,-2,0,
%U A100219 1,0,-2,-3,-2,0,1,0,-2,-3,-2,0,1,0,-2,-3,-2,0
%N A100219 Expansion of (1-2*x)/((1-x)*(1-x+x^2)).
%C A100219 Row sums of number triangle A100218.
%H A100219 G. C. Greubel, <a href="/A100219/b100219.txt">Table of n, a(n) for n = 0..10000</a>
%H A100219 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,1).
%F A100219 a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3).
%F A100219 a(n) = cos(Pi*n/3 + Pi/3) + sqrt(3)*sin(Pi*n/3 + Pi/3) - 1.
%F A100219 a(n) is the n-th order Taylor polynomial (centered at 0) of 1/c(x)^n evaluated at x = 1, where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. of the Catalan numbers A000108. - _Peter Bala_, Apr 20 2024
%t A100219 PadRight[{}, 120, {1,0,-2,-3,-2,0}] (* or *) LinearRecurrence[{2,-2,1}, {1,0,-2}, 50] (* _G. C. Greubel_, Mar 13 2017; Mar 28 2024 *)
%t A100219 Table[Cos[Pi*n/3 + Pi/3] + Sqrt[3]*Sin[Pi*n/3 + Pi/3] - 1, {n, 0, 71}] (* _Indranil Ghosh_, Mar 13 2017 *)
%o A100219 (PARI) my(x='x+O('x^50)); Vec((1-2*x)/((1-x)*(1-x+x^2))) \\ _G. C. Greubel_, Mar 13 2017
%o A100219 (Magma) &cat[[1,0,-2,-3,-2,0]: n in [0..20]]; // _G. C. Greubel_, Mar 28 2024
%o A100219 (SageMath)
%o A100219 def A100219(n): return [1,0,-2,-3,-2,0][n%6]
%o A100219 [A100219(n) for n in range(121)] # _G. C. Greubel_, Mar 28 2024
%Y A100219 Cf. A079757, A100218.
%K A100219 easy,sign
%O A100219 0,3
%A A100219 _Paul Barry_, Nov 08 2004