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Molien series for 3-dimensional group [2,5] = *225.
2

%I #19 Sep 08 2022 08:44:36

%S 1,0,2,0,3,1,4,2,5,3,7,4,9,5,11,7,13,9,15,11,18,13,21,15,24,18,27,21,

%T 30,24,34,27,38,30,42,34,46,38,50,42,55,46,60,50,65,55,70,60,75,65,81,

%U 70,87,75,93,81,99,87,105,93,112,99,119,105,126,112,133,119,140,126,148,133,156

%N Molien series for 3-dimensional group [2,5] = *225.

%H G. C. Greubel, <a href="/A008720/b008720.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=223">Encyclopedia of Combinatorial Structures 223</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 (0,2,0,-1,1,0,-2,0,1).

%p 1/((1-x^2)^2*(1-x^5)); seq(coeff(series(%, x, n+1), x, n), n = 0 .. 80); # modified by _G. C. Greubel_, Sep 09 2019

%t LinearRecurrence[{0,2,0,-1,1,0,-2,0,1}, {1,0,2,0,3,1,4,2,5}, 80] (* _Harvey P. Dale_, Dec 10 2015 *)

%o (PARI) my(x='x+O('x^80)); Vec(1/((1-x^2)^2*(1-x^5))) \\ _G. C. Greubel_, Sep 09 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^2)^2*(1-x^5)) )); // _G. C. Greubel_, Sep 09 2019

%o (Sage)

%o def A008720_list(prec):

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

%o return P(1/((1-x^2)^2*(1-x^5))).list()

%o A008720_list(80) # _G. C. Greubel_, Sep 09 2019

%o (GAP) a:=[1,0,2,0,3,1,4,2,5];; for n in [10..80] do a[n]:=2*a[n-2]-a[n-4] +a[n-5]-2*a[n-7]+a[n-9]; od; a; # _G. C. Greubel_, Sep 09 2019

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E Terms a(65) onward added by _G. C. Greubel_, Sep 09 2019