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 A078014 #17 Sep 08 2022 08:45:08
%S A078014 1,0,0,-2,-2,-2,2,6,10,6,-6,-26,-38,-26,26,102,154,102,-102,-410,-614,
%T A078014 -410,410,1638,2458,1638,-1638,-6554,-9830,-6554,6554,26214,39322,
%U A078014 26214,-26214,-104858,-157286,-104858,104858,419430,629146,419430,-419430,-1677722,-2516582,-1677722,1677722
%N A078014 Expansion of (1-x)/(1-x+2*x^3).
%H A078014 G. C. Greubel, <a href="/A078014/b078014.txt">Table of n, a(n) for n = 0..1000</a>
%H A078014 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,-2).
%F A078014 G.f.: (1-x)/(1-x+2*x^3).
%F A078014 G.f.: G(0)/(2*(1+x)), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+2) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, May 25 2013
%F A078014 a(n) = A077950(n) - A077950(n-1). - _R. J. Mathar_, Jul 21 2016
%t A078014 LinearRecurrence[{1,0,-2}, {1,0,0}, 50] (* or *) CoefficientList[Series[ (1-x)/(1-x+2*x^3), {x,0,50}], x] (* _G. C. Greubel_, Jun 29 2019 *)
%o A078014 (PARI) my(x='x+O('x^50)); Vec((1-x)/(1-x+2*x^3)) \\ _G. C. Greubel_, Jun 29 2019
%o A078014 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x+2*x^3) )); // _G. C. Greubel_, Jun 29 2019
%o A078014 (Sage) ((1-x)/(1-x+2*x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 29 2019
%o A078014 (GAP) a:=[1,0,0];; for n in [4..50] do a[n]:=a[n-1]-2*a[n-3]; od; a; # _G. C. Greubel_, Jun 29 2019
%Y A078014 Cf. A077950.
%K A078014 sign,easy
%O A078014 0,4
%A A078014 _N. J. A. Sloane_, Nov 17 2002