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 A176563 #41 Dec 12 2023 07:40:18
%S A176563 1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,
%T A176563 1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,
%U A176563 -3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1,-3,1,1,1
%N A176563 Period 4: repeat [1, -3, 1, 1].
%H A176563 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1).
%F A176563 Sum_{k>=0} a(k)/(k+1) = 0.
%F A176563 a(n) = cos(n*Pi) - 2*sin(n*Pi/2).
%F A176563 G.f.: (1-2*x-x^2)/((1+x)*(1+x^2)).
%F A176563 a(n) = -a(n-1) -a(n-2) -a(n-3) for n>2. [_R. J. Mathar_, Apr 28 2010]
%F A176563 a(n) = 1-(1-(-1)^n)*(1-I^(n+1)). - _Bruno Berselli_, Mar 16 2011
%F A176563 Dirichlet generating function: Zeta(s)*(1 - 1/2^(s - 1))^2. [_Mats Granvik_ and _Jaume Oliver Lafont_, Mar 12 2014]
%F A176563 a(n) = a(n-4) for n>3. - _Wesley Ivan Hurt_, Jul 07 2016
%F A176563 E.g.f.: exp(-x) - 2*sin(x). - _Ilya Gutkovskiy_, Jul 07 2016
%p A176563 seq(op([1, -3, 1, 1]), n=0..50); # _Wesley Ivan Hurt_, Jul 07 2016
%t A176563 PadRight[{}, 100, {1, -3, 1, 1}] (* _Wesley Ivan Hurt_, Jul 07 2016 *)
%o A176563 (PARI) a(n)=[1,-3,1,1][n%4+1]
%o A176563 (Magma) &cat [[1, -3, 1, 1]^^30]; // _Wesley Ivan Hurt_, Jul 07 2016
%K A176563 sign,easy
%O A176563 0,2
%A A176563 _Jaume Oliver Lafont_, Apr 20 2010