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A008648 Molien series of 3 X 3 upper triangular matrices over GF( 5 ).

%I A008648 #23 Sep 08 2022 08:44:36
%S A008648 1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,7,7,7,7,7,9,9,9,9,
%T A008648 9,11,11,11,11,11,13,13,13,13,13,15,15,15,15,15,18,18,18,18,18,21,21,
%U A008648 21,21,21,24,24,24,24,24
%N A008648 Molien series of 3 X 3 upper triangular matrices over GF( 5 ).
%C A008648 a(n) is the number of partitions of n into parts 1, 5, and 25. - _Joerg Arndt_, Sep 07 2019
%D A008648 D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
%H A008648 G. C. Greubel, <a href="/A008648/b008648.txt">Table of n, a(n) for n = 0..1000</a>
%H A008648 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=221">Encyclopedia of Combinatorial Structures 221</a>
%H A008648 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H A008648 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 1).
%F A008648 G.f.: 1/((1-x)*(1-x^5)*(1-x^25)).
%p A008648 seq(coeff(series(1/((1-x)*(1-x^5)*(1-x^25)), x, n+1), x, n), n = 0 .. 70); # modified by _G. C. Greubel_, Sep 06 2019
%t A008648 CoefficientList[Series[1/((1-x)*(1-x^5)*(1-x^25)), {x,0,70}], x] (* _G. C. Greubel_, Sep 06 2019 *)
%o A008648 (PARI) my(x='x+O('x^70)); Vec(1/((1-x)*(1-x^5)*(1-x^25))) \\ _G. C. Greubel_, Sep 06 2019
%o A008648 (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)*(1-x^5)*(1-x^25)) )); // _G. C. Greubel_, Sep 06 2019
%o A008648 (Sage)
%o A008648 def A008648_list(prec):
%o A008648     P.<x> = PowerSeriesRing(ZZ, prec)
%o A008648     return P(1/((1-x)*(1-x^5)*(1-x^25))).list()
%o A008648 A008648_list(70) # _G. C. Greubel_, Sep 06 2019
%Y A008648 Cf. A002266.
%K A008648 nonn,easy
%O A008648 0,6
%A A008648 _N. J. A. Sloane_