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%I #19 Mar 31 2023 13:52:51
%S 1,-1,-1,-1,3,3,-1,-9,-5,11,23,-1,-45,-45,47,135,43,-229,-313,143,771,
%T 483,-1057,-2025,91,4139,3959,-4321,-12237,-3597,20879,28071,-13685,
%U -69829,-42457,97199,182115,-12285,-376513,-351945,401083,1104971,302807,-1907137,-2512749,1301523,6327023
%N Expansion of (1-x) / (1+x^2+2*x^3).
%H Colin Barker, <a href="/A078033/b078033.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,-1,-2).
%F 2*((-1)^n)*a(n) + A001607(n+2) = 1 - _Creighton Dement_, Oct 30 2004
%F a(n) = -a(n-2) - 2*a(n-3) for n>2. - _Colin Barker_, May 18 2019
%p seq(coeff(series((1-x)/((1+x)*(1-x+2*x^2)), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Nov 22 2019
%t LinearRecurrence[{0,-1,-2}, {1,-1,-1}, 40] (* _G. C. Greubel_, Nov 22 2019 *)
%t CoefficientList[Series[(1-x)/(1+x^2+2x^3),{x,0,60}],x] (* _Harvey P. Dale_, Mar 31 2023 *)
%o (PARI) Vec((1-x)/((1+x)*(1-x+2*x^2)) + O(x^40)) \\ _Colin Barker_, May 18 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/((1+x)*(1-x+2*x^2)) )); // _G. C. Greubel_, Nov 22 2019
%o (Sage)
%o def A078033_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1-x)/((1+x)*(1-x+2*x^2)) ).list()
%o A078033_list(40) # _G. C. Greubel_, Nov 22 2019
%o (GAP) a:=[1,-1,-1];; for n in [4..40] do a[n]:=-a[n-2]-2*a[n-3]; od; a; # _G. C. Greubel_, Nov 22 2019
%K sign,easy
%O 0,5
%A _N. J. A. Sloane_, Nov 17 2002
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