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 A105385 #26 Dec 14 2023 05:17:39
%S A105385 1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,
%T A105385 0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,
%U A105385 -1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1
%N A105385 Expansion of (1-x^2)/(1-x^5).
%C A105385 Periodic {1,0,-1,0,0}.
%C A105385 Binomial transform is A103311(n+1). Consecutive pair sums of A105384.
%H A105385 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,-1).
%F A105385 G.f.: (1+x)/(1 + x + x^2 + x^3 + x^4);
%F A105385 a(n) = sqrt(1/5 - 2*sqrt(5)/25)*cos(4*Pi*n/5 + Pi/10) + sqrt(5)*sin(4*Pi*n/5 + Pi/10)/5 + sqrt(2*sqrt(5)/25 + 1/5)*cos(2*Pi*n/5 + 3*Pi/10) + sqrt(5)*sin(2*Pi*n/5 + 3*Pi/10)/5.
%F A105385 a(n) = A092202(n+1). - _R. J. Mathar_, Aug 28 2008
%F A105385 a(n) = a(n-1) - a(n-2) - a(n-3) - a(n-4); a(0)=1, a(1)=0, a(2)=-1, a(3)=0. - _Harvey P. Dale_, Mar 10 2013
%t A105385 CoefficientList[Series[(1-x^2)/(1-x^5),{x,0,100}],x] (* or *) PadRight[{},100,{1,0,-1,0,0}] (* or *) LinearRecurrence[{-1,-1,-1,-1},{1,0,-1,0},100] (* _Harvey P. Dale_, Mar 10 2013 *)
%Y A105385 Cf. A092202 (essentially the same).
%Y A105385 Cf. A198517 (absolute values).
%Y A105385 Cf. A103311, A105384
%K A105385 sign,easy
%O A105385 0,1
%A A105385 _Paul Barry_, Apr 02 2005