%I #19 Sep 08 2022 08:44:36
%S 1,0,2,0,3,0,4,0,6,1,8,2,10,3,12,4,15,6,18,8,21,10,24,12,28,15,32,18,
%T 36,21,40,24,45,28,50,32,55,36,60,40,66,45,72,50,78,55,84,60,91,66,98,
%U 72,105,78,112,84,120,91,128,98,136,105,144,112,153,120,162,128,171,136,180,144,190,153
%N Molien series for group [2,8]+ = 228.
%H G. C. Greubel, <a href="/A008801/b008801.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,0,0,0,1,-1,-1,1).
%F G.f.: (1+x^9)/((1-x^2)^2*(1-x^8)).
%F G.f.: (1-x+x^2)*(1-x^3+x^6)/( (1+x^2)*(1+x^4)*(1+x)^2*(1-x)^3 ). - _R. J. Mathar_, Dec 18 2014
%p seq(coeff(series((1+x^9)/((1-x^2)^2*(1-x^8)), x, n+1), x, n), n = 0..80);
%t CoefficientList[Series[(1+x^9)/((1-x^2)^2*(1-x^8)), {x,0,80}], x] (* _G. C. Greubel_, Sep 12 2019 *)
%o (PARI) my(x='x+O('x^80)); Vec((1+x^9)/((1-x^2)^2*(1-x^8))) \\ _G. C. Greubel_, Sep 12 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^9)/((1-x^2)^2*(1-x^8)) )); // _G. C. Greubel_, Sep 12 2019
%o (Sage)
%o def A008801_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1+x^9)/((1-x^2)^2*(1-x^8))).list()
%o A008801_list(80) # _G. C. Greubel_, Sep 12 2019
%o (GAP) a:=[1,0,2,0,3,0,4,0,6,1,8];; for n in [12..80] do a[n]:=a[n-1] +a[n-2]-a[n-3]+a[n-8]-a[n-9]-a[n-10]+a[n-11]; od; a; # _G. C. Greubel_, Sep 12 2019
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E More terms added by _G. C. Greubel_, Sep 12 2019