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A008734 Molien series for 3-dimensional group [2+,n ] = 2*(n/2). 1

%I #18 Sep 08 2022 08:44:36

%S 1,0,2,0,3,1,4,2,6,3,8,4,10,6,12,8,15,10,18,12,21,15,24,18,28,21,32,

%T 24,36,28,40,32,45,36,50,40,55,45,60,50,66,55,72,60,78,66,84,72,91,78,

%U 98,84,105,91,112,98,120

%N Molien series for 3-dimensional group [2+,n ] = 2*(n/2).

%H G. C. Greubel, <a href="/A008734/b008734.txt">Table of n, a(n) for n = 0..10000</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 +x^2 -x^3 +x^4)/((1+x^2)*(1+x^4)*(1+x)^2*(1-x)^3). - _R. J. Mathar_, Dec 18 2014

%p seq(coeff(series((1+x^5)/((1-x^2)^2*(1-x^8)), x, n+1), x, n), n = 0 .. 70); # modified by _G. C. Greubel_, Jul 30 2019

%t CoefficientList[Series[(1+x^5)/((1-x^2)^2*(1-x^8)), {x,0,70}], x] (* _G. C. Greubel_, Jul 30 2019 *)

%o (PARI) my(x='x+O('x^70)); Vec((1+x^5)/((1-x^2)^2*(1-x^8))) \\ _G. C. Greubel_, Jul 30 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^5)/((1-x^2)^2*(1-x^8)) )); // _G. C. Greubel_, Jul 30 2019

%o (Sage) ((1+x^5)/((1-x^2)^2*(1-x^8))).series(x, 70).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 30 2019

%o (GAP) a:=[1,0,2,0,3,1,4,2,6,3,8];; for n in [12..70] 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_, Jul 30 2019

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)