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Molien series for group [2,7]+ = 227.
1

%I #23 Sep 08 2022 08:44:36

%S 1,0,2,0,3,0,4,1,6,2,8,3,10,4,13,6,16,8,19,10,22,13,26,16,30,19,34,22,

%T 39,26,44,30,49,34,54,39,60,44,66,49,72,54,79,60,86,66,93,72,100,79,

%U 108,86,116,93,124,100,133,108,142,116,151,124,160,133,170,142,180,151,190,160,201,170

%N Molien series for group [2,7]+ = 227.

%H G. C. Greubel, <a href="/A008800/b008800.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 (0,2,0,-1,0,0,1,0,-2,0,1).

%F G.f.: (1+x^8)/((1-x^2)^2 * (1-x^7)).

%p seq(coeff(series((1+x^8)/((1-x^2)^2*(1-x^7)), x, n+1), x, n), n = 0..80);

%t CoefficientList[Series[(1+x^8)/((1-x^2)^2*(1-x^7)), {x,0,80}], x] (* _G. C. Greubel_, Sep 12 2019 *)

%t LinearRecurrence[{0,2,0,-1,0,0,1,0,-2,0,1},{1,0,2,0,3,0,4,1,6,2,8},80] (* _Harvey P. Dale_, Jul 07 2021 *)

%o (PARI) my(x='x+O('x^80)); Vec((1+x^8)/((1-x^2)^2*(1-x^7))) \\ _G. C. Greubel_, Sep 12 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^8)/((1-x^2)^2*(1-x^7)) )); // _G. C. Greubel_, Sep 12 2019

%o (Sage)

%o def A008800_list(prec):

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

%o return P((1+x^8)/((1-x^2)^2*(1-x^7))).list()

%o A008800_list(80) # _G. C. Greubel_, Sep 12 2019

%o (GAP) a:=[1,0,2,0,3,0,4,1,6,2,8];; for n in [12..80] do a[n]:=2*a[n-2] -a[n-4]+a[n-7]-2*a[n-9]+a[n-11]; 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