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%I #12 Sep 08 2022 08:45:07
%S 1,0,-1,3,0,-6,10,3,-28,33,27,-120,100,168,-487,252,891,-1881,352,
%T 4302,-6886,-1365,19440,-23595,-16649,83280,-73576,-109632,340065,
%U -194376,-595385,1324203,-327808,-2915982,4895802,608355,-13315940,16995033,10245203,-57551208,54055836,71291784
%N Expansion of 1/((1-x)*(1+x+2*x^2-x^3)).
%H G. C. Greubel, <a href="/A077911/b077911.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,3,-1).
%t LinearRecurrence[{0,-1,3,-1}, {1,0,-1,3}, 50] (* or *) CoefficientList[ Series[1/((1-x)*(1+x+2*x^2-x^3)), {x,0,50}], x] (* _G. C. Greubel_, Jul 02 2019 *)
%o (PARI) Vec(1/((1-x)*(1+x+2*x^2-x^3))+O(x^50)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1-x)*(1+x+2*x^2-x^3)) )); // _G. C. Greubel_, Jul 02 2019
%o (Sage) (1/((1-x)*(1+x+2*x^2-x^3))).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 02 2019
%o (GAP) a:=[1,0,-1,3];; for n in [4..50] do a[n]:=-a[n-2]+3*a[n-3]-a[n-4]; od; a; # _G. C. Greubel_, Jul 02 2019
%Y Cf. A077978.
%K sign,easy
%O 0,4
%A _N. J. A. Sloane_, Nov 17 2002
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