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 A199804 #25 Jan 05 2025 19:51:39
%S A199804 1,-1,1,-2,3,-4,6,-9,13,-19,28,-41,60,-88,129,-189,277,-406,595,-872,
%T A199804 1278,-1873,2745,-4023,5896,-8641,12664,-18560,27201,-39865,58425,
%U A199804 -85626,125491,-183916,269542,-395033,578949,-848491,1243524,-1822473,2670964,-3914488,5736961,-8407925,12322413,-18059374,26467299,-38789712,56849086,-83316385
%N A199804 G.f.: 1/(1+x+x^3).
%C A199804 There are several similar sequences already in the OEIS, but this one warrants its own entry because it is one of Hirschhorn's family.
%H A199804 G. C. Greubel, <a href="/A199804/b199804.txt">Table of n, a(n) for n = 0..1000</a>
%H A199804 Michael D. Hirschhorn, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/43-4/paper43-4-5.pdf">Non-trivial intertwined second-order recurrence relations</a>, Fibonacci Quart. 43 (2005), no. 4, 316-325. See K_n.
%H A199804 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 0, -1).
%F A199804 a(n) = (-1)^n*A000930(n). - _R. J. Mathar_, Jul 10 2012
%F A199804 G.f.: 1 - x/(G(0) + x) where G(k) = 1 - x^2/(1 - x^2/(x^2 - 1/G(k+1) )); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Dec 16 2012
%F A199804 G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1 - x*(4*k+1 + x^2)/( x*(4*k+3 + x^2) - 1/Q(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Sep 08 2013
%F A199804 a(0)=1, a(1)=-1, a(2)=1, a(n)=a(n-1)-a(n-3). - _Harvey P. Dale_, Feb 18 2016
%t A199804 CoefficientList[Series[1/(1+x+x^3),{x,0,50}],x] (* or *) LinearRecurrence[ {-1,0,-1},{1,-1,1},50] (* _Harvey P. Dale_, Feb 18 2016 *)
%o A199804 (PARI) x='x+O('x^50); Vec(1/(1+x+x^3)) \\ _G. C. Greubel_, Apr 29 2017
%K A199804 sign
%O A199804 0,4
%A A199804 _N. J. A. Sloane_, Nov 10 2011