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%I #10 Sep 08 2022 08:45:08
%S 1,-1,0,-2,2,0,4,-4,0,-8,8,0,16,-16,0,-32,32,0,64,-64,0,-128,128,0,
%T 256,-256,0,-512,512,0,1024,-1024,0,-2048,2048,0,4096,-4096,0,-8192,
%U 8192,0,16384,-16384,0,-32768,32768,0,65536,-65536,0,-131072,131072,0,262144,-262144,0,-524288,524288,0
%N Expansion of (1-x)/(1+2*x^3).
%H G. C. Greubel, <a href="/A078030/b078030.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 (0,0,-2).
%p seq(coeff(series((1-x)/(1+2*x^3), x, n+1), x, n), n = 0..60); # _G. C. Greubel_, Aug 05 2019
%t CoefficientList[Series[(1-x)/(1+2*x^3), {x,0,60}], x] (* _G. C. Greubel_, Aug 05 2019 *)
%o (PARI) my(x='x+O('x^60)); Vec((1-x)/(1+2*x^3)) \\ _G. C. Greubel_, Aug 05 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x)/(1+2*x^3) )); // _G. C. Greubel_, Aug 05 2019
%o (Sage) ((1-x)/(1+2*x^3)).series(x, 60).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 05 2019
%o (GAP) a:=[1,-1,0];; for n in [4..60] do a[n]:=-2*a[n-3]; od; a; # _G. C. Greubel_, Aug 05 2019
%K sign
%O 0,4
%A _N. J. A. Sloane_, Nov 17 2002
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