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A008650 Molien series of 4 X 4 upper triangular matrices over GF( 3 ).

%I A008650 #21 Sep 08 2022 08:44:36
%S A008650 1,1,1,2,2,2,3,3,3,5,5,5,7,7,7,9,9,9,12,12,12,15,15,15,18,18,18,23,23,
%T A008650 23,28,28,28,33,33,33,40,40,40,47,47,47,54,54,54,63,63,63,72,72,72,81,
%U A008650 81,81,93,93,93,105,105
%N A008650 Molien series of 4 X 4 upper triangular matrices over GF( 3 ).
%D A008650 D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
%H A008650 G. C. Greubel, <a href="/A008650/b008650.txt">Table of n, a(n) for n = 0..1000</a>
%H A008650 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=235">Encyclopedia of Combinatorial Structures 235</a>
%H A008650 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H A008650 <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 1, -1).
%F A008650 a(n) ~ 1/4374*n^3. - _Ralf Stephan_, Apr 29 2014
%F A008650 G.f.: 1/((1-x)*(1-x^3)*(1-x^9)*(1-x^27)).
%p A008650 1/((1-x)*(1-x^3)*(1-x^9)*(1-x^27)): seq(coeff(series(%, x, n+1), x, n), n=0..70);
%t A008650 CoefficientList[Series[1/((1-x)*(1-x^3)*(1-x^9)*(1-x^27)), {x,0,70}], x] (* _G. C. Greubel_, Sep 06 2019 *)
%o A008650 (PARI) my(x='x+O('x^70)); Vec(1/((1-x)*(1-x^3)*(1-x^9)*(1-x^27))) \\ _G. C. Greubel_, Sep 06 2019
%o A008650 (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)*(1-x^3)*(1-x^9)*(1-x^27)) )); // _G. C. Greubel_, Sep 06 2019
%o A008650 (Sage)
%o A008650 def A008650_list(prec):
%o A008650     P.<x> = PowerSeriesRing(ZZ, prec)
%o A008650     return P(1/((1-x)*(1-x^3)*(1-x^9)*(1-x^27))).list()
%o A008650 A008650_list(70) # _G. C. Greubel_, Sep 06 2019
%K A008650 nonn,easy
%O A008650 0,4
%A A008650 _N. J. A. Sloane_