|
%I #14 Jun 13 2015 00:51:01
%S 1,0,1,2,3,4,5,6,9,10,13,14,17,20,23,26,29,32,37,40,45,48,53,58,63,68,
%T 73,78,85,90,97,102,109,116,123,130,137,144,153,160,169,176,185,194,
%U 203,212,221,230,241,250,261,270,281,292,303,314,325,336,349,360,373,384,397,410
%N Expansion of Molien series for 5-dimensional representation of dihedral group of order 10.
%D M. D. Neusel and L. Smith, Invariant Theory of Finite Groups, Amer. Math. Soc., 2002; see p. 149.
%H Vincenzo Librandi, <a href="/A082642/b082642.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,1,-1,-1,1).
%F G.f.: (1+x^2+x^3+2*x^4+2*x^5+2*x^6+x^7+x^8+x^10)/((1-x^3)*(1-x^4)*(1-x^5)).
%F G.f.: -(x^6-x^5+2*x^3-x+1) / ((x-1)^3*(x+1)*(x^4+x^3+x^2+x+1)). - _Colin Barker_, Apr 02 2015
%t CoefficientList[Series[(1 + x^2 + x^3 + 2 x^4 + 2 x^5 + 2 x^6 + x^7 + x^8 +x^10) / ((1 - x^3) (1 - x^4) (1 - x^5)), {x, 0, 70}], x] (* _Vincenzo Librandi_, Aug 15 2013 *)
%o (PARI) Vec(-(x^6-x^5+2*x^3-x+1)/((x-1)^3*(x+1)*(x^4+x^3+x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Apr 02 2015
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, May 15 2003
|
