Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #28 Sep 08 2022 08:44:36
%S 1,1,1,2,2,2,3,3,3,5,5,5,7,7,7,9,9,9,12,12,12,15,15,15,18,18,18,22,22,
%T 22,26,26,26,30,30,30,35,35,35,40,40,40,45,45,45,51,51,51,57,57,57,63,
%U 63,63,70,70,70,77,77,77,84,84,84,92,92,92,100,100,100
%N Molien series of 3 X 3 upper triangular matrices over GF( 3 ).
%C Number of partitions of n into parts 1, 3 or 9. - _Reinhard Zumkeller_, Aug 12 2011
%D D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
%H G. C. Greubel, <a href="/A008649/b008649.txt">Table of n, a(n) for n = 0..1000</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=219">Encyclopedia of Combinatorial Structures 219</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, -1, 1).
%F G.f.: 1/((1-x)*(1-x^3)*(1-x^9)).
%F a(n) = floor((6*(floor(n/3) +1)*(3*floor(n/3) -n +1) +n^2 +13*n +58)/54). - _Tani Akinari_, Jul 12 2013
%p 1/((1-x)*(1-x^3)*(1-x^9)): seq(coeff(series(%,x,n+1),x,n), n=0..70);
%t CoefficientList[Series[1/((1-x)*(1-x^3)*(1-x^9)), {x,0,70}], x] (* _G. C. Greubel_, Sep 06 2019 *)
%o (PARI) my(x='x+O('x^70)); Vec(1/((1-x)*(1-x^3)*(1-x^9))) \\ _G. C. Greubel_, Sep 06 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)*(1-x^3)*(1-x^9)) )); // _G. C. Greubel_, Sep 06 2019
%o (Sage)
%o def A008649_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P(1/((1-x)*(1-x^3)*(1-x^9))).list()
%o A008649_list(70) # _G. C. Greubel_, Sep 06 2019
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_