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A008799 Molien series for group [2,6]+ = 226. 1

%I #31 Sep 08 2022 08:44:36

%S 1,0,2,0,3,0,5,1,7,2,9,3,12,5,15,7,18,9,22,12,26,15,30,18,35,22,40,26,

%T 45,30,51,35,57,40,63,45,70,51,77,57,84,63,92,70,100,77,108,84,117,92,

%U 126,100,135,108,145,117,155,126,165,135,176,145,187,155,198,165,210,176,222,187

%N Molien series for group [2,6]+ = 226.

%H G. C. Greubel, <a href="/A008799/b008799.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_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,0,1,-1,-1,1).

%F G.f.: (1+x^7)/((1-x^2)^2*(1-x^6)).

%F a(n) = floor((n^2+3*n+21+7*(n+1)*(-1)^n)/24). - _Tani Akinari_, Jul 25 2013

%F G.f.: (1 -x +x^2 -x^3 +x^4 -x^5 +x^6)/( (1+x+x^2)*(1-x+x^2)*(1+x)^2*(1-x)^3 ). - _R. J. Mathar_, Dec

%F 18 2014

%p seq(coeff(series((1+x^7)/((1-x^2)^2*(1-x^6)), x, n+1), x, n), n = 0..80);

%t CoefficientList[Series[(1+x^7)/((1-x^2)^2*(1-x^6)), {x,0,80}], x] (* _G. C. Greubel_, Sep 12 2019 *)

%t LinearRecurrence[{1,1,-1,0,0,1,-1,-1,1},{1,0,2,0,3,0,5,1,7},80] (* _Harvey P. Dale_, Apr 16 2022 *)

%o (PARI) my(x='x+O('x^80)); Vec((1+x^7)/((1-x^2)^2*(1-x^6))) \\ _G. C. Greubel_, Sep 12 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^7)/((1-x^2)^2*(1-x^6)) )); // _G. C. Greubel_, Sep 12 2019

%o (Sage)

%o def A008799_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P((1+x^7)/((1-x^2)^2*(1-x^6))).list()

%o A008799_list(80) # _G. C. Greubel_, Sep 12 2019

%o (GAP) a:=[1,0,2,0,3,0,5,1,7];; for n in [10..80] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-6]-a[n-7]-a[n-8]+a[n-9]; od; a; # _G. C. Greubel_, Sep 12 2019

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E Definition clarified by _N. J. A. Sloane_, Feb 02 2018

%E More terms added by _G. C. Greubel_, Sep 12 2019

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Last modified March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)