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 A100285 #26 May 11 2024 17:33:27
%S A100285 1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,
%T A100285 5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,
%U A100285 1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1,5,5,1,1
%N A100285 Expansion of (1+5*x^2)/(1-x+x^2-x^3).
%C A100285 This sequence is periodic. - _T. D. Noe_, Nov 09 2006
%C A100285 Decimal expansion of 35/303. - _Elmo R. Oliveira_, May 11 2024
%H A100285 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1).
%F A100285 a(n) = a(n-1) - a(n-2) + a(n-3)
%F A100285 a(n) = 3 - 2*cos(Pi*n/2) - 2*sin(Pi*n/2).
%F A100285 a(n) = mod(A100284(n), 8).
%F A100285 From _G. C. Greubel_, Feb 06 2023: (Start)
%F A100285 a(n) = A133872(n) + 5*A133872(n+2).
%F A100285 a(n) = ((n+2 mod 4) + 5*(n mod 4) - 6*(n mod 2))/2.
%F A100285 a(n) = 3 -((1+i)*(-1)^n +(1-i)*i^n) = 3 -2*(A056594(n) +A056594(n-1)).
%F A100285 G.f.: (1+5*x^2)/((1-x)*(1+x^2)).
%F A100285 E.g.f.: 3*exp(x) - 2*cos(x) - 2*sin(x). (End)
%t A100285 CoefficientList[Series[(1+5x^2)/(1-x+x^2-x^3),{x,0,100}],x] (* or *) PadRight[{},100,{1,1,5,5}] (* _Harvey P. Dale_, Jun 02 2021 *)
%o A100285 (Magma) [(((n+2) mod 4) + 5*(n mod 4) - 6*(n mod 2))/2: n in [0..100]]; // _G. C. Greubel_, Feb 06 2023
%o A100285 (SageMath)
%o A100285 def A100285(n): return (((n+2)%4) +5*(n%4) -6*(n%2))/2
%o A100285 [A100285(n) for n in range(101)] # _G. C. Greubel_, Feb 06 2023
%Y A100285 Cf. A056594, A100284, A133872.
%K A100285 nonn,easy
%O A100285 0,3
%A A100285 _Paul Barry_, Nov 11 2004
%E A100285 Corrected by _T. D. Noe_, Nov 09 2006