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%I #13 Sep 08 2022 08:45:08
%S 1,-1,2,-4,6,-12,20,-36,64,-112,200,-352,624,-1104,1952,-3456,6112,
%T -10816,19136,-33856,59904,-105984,187520,-331776,587008,-1038592,
%U 1837568,-3251200,5752320,-10177536,18007040,-31859712,56369152,-99733504,176457728,-312205312,552382464
%N Expansion of (1-x)/(1-2*x^2+2*x^3).
%H G. C. Greubel, <a href="/A078025/b078025.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,-2)
%p seq(coeff(series((1-x)/(2*x^3-2*x^2+1), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Aug 04 2019
%t CoefficientList[Series[(1-x)/(1-2*x^2+2*x^3), {x,0,40}], x] (* _G. C. Greubel_, Aug 04 2019 *)
%o (PARI) Vec((1-x)/(1-2*x^2+2*x^3)+O(x^40)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-2*x^2+2*x^3) )); // _G. C. Greubel_, Aug 04 2019
%o (Sage) ((1-x)/(1-2*x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 04 2019
%o (GAP) a:=[1,-1,2];; for n in [4..40] do a[n]:=2*a[n-2]-2*a[n-3]; od; a; # _G. C. Greubel_, Aug 04 2019
%K sign,easy
%O 0,3
%A _N. J. A. Sloane_, Nov 17 2002
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