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%I #11 Sep 08 2022 08:44:36
%S 1,0,2,0,3,2,4,4,5,6,8,8,11,10,14,14,17,18,20,22,25,26,30,30,35,36,40,
%T 42,45,48,52,54,59,60,66,68,73,76,80,84,89,92,98,100,107,110,116,120,
%U 125,130,136,140,147,150,158,162,169,174,180,186,193,198,206
%N Expansion of (1+x^5)/((1-x^2)^2*(1-x^5)).
%H G. C. Greubel, <a href="/A008807/b008807.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,1,-1,-1,1).
%F G.f.: (1+x^5)/((1-x^2)^2*(1-x^5)). - _G. C. Greubel_, Sep 12 2019
%p seq(coeff(series((1+x^5)/((1-x^2)^2*(1-x^5)), x, n+1), x, n), n = 0..70); # _G. C. Greubel_, Sep 12 2019
%t CoefficientList[Series[(1+x^5)/((1-x^2)^2*(1-x^5)), {x,0,70}], x] (* or *) LinearRecurrence[{1,1,-1,0,1,-1,-1,1}, {1,0,2,0,3,2,4,4}, 70] (* _G. C. Greubel_, Sep 12 2019 *)
%o (PARI) my(x='x+O('x^70)); Vec((1+x^5)/((1-x^2)^2*(1-x^5))) \\ _G. C. Greubel_, Sep 12 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^5)/((1-x^2)^2*(1-x^5)) )); // _G. C. Greubel_, Sep 12 2019
%o (Sage)
%o def A008807_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1+x^5)/((1-x^2)^2*(1-x^5))).list()
%o A008807_list(70) # _G. C. Greubel_, Sep 12 2019
%o (GAP) a:=[1,0,2,0,3,2,4,4];; for n in [9..70] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-5]-a[n-6]-a[n-7]+a[n-8]; od; a; # _G. C. Greubel_, Sep 12 2019
%K nonn
%O 0,3
%A _N. J. A. Sloane_
%E More terms added by _G. C. Greubel_, Sep 12 2019
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