%I #20 Sep 08 2022 08:44:36
%S 1,0,2,0,3,0,4,0,5,1,7,2,9,3,11,4,13,5,16,7,19,9,22,11,25,13,28,16,32,
%T 19,36,22,40,25,44,28,49,32,54,36,59,40,64,44,69,49,75,54,81,59,87,64,
%U 93,69,100,75,107,81,114,87,121,93,128,100,136,107,144,114
%N Molien series for group [2,9]+ = 229.
%H G. C. Greubel, <a href="/A008802/b008802.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_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1,0,0,0,0,1,0,-2,0,1).
%F G.f.: (1+x^10)/((1-x^2)^2*(1-x^9)).
%p seq(coeff(series((1+x^10)/((1-x^2)^2*(1-x^9)), x, n+1), x, n), n = 0..80);
%t CoefficientList[Series[(1+x^10)/(1-x^2)^2/(1-x^9),{x,0,80}],x] (* _Harvey P. Dale_, Nov 28 2012 *)
%t LinearRecurrence[{0,2,0,-1,0,0,0,0,1,0,-2,0,1}, {1,0,2,0,3,0,4,0,5,1, 7,2}, 80] (* _G. C. Greubel_, Sep 12 2019 *)
%o (PARI) my(x='x+O('x^80)); Vec((1+x^10)/((1-x^2)^2*(1-x^9))) \\ _G. C. Greubel_, Sep 12 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^10)/((1-x^2)^2*(1-x^9)) )); // _G. C. Greubel_, Sep 12 2019
%o (Sage)
%o def A008802_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1+x^10)/((1-x^2)^2*(1-x^9))).list()
%o A008802_list(80) # _G. C. Greubel_, Sep 12 2019
%o (GAP) a:=[1,0,2,0,3,0,4,0,5,1,7,2];; for n in [13..80] do a[n]:=2*a[n-2] -a[n-4]+a[n-9]-2*a[n-10]+a[n-12]; 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