A104993 - OEIS

%I #11 Sep 08 2022 08:45:17

%S 1,2,4,8,16,31,61,117,224,424,796,1476,2717,4938,8876,15756,27616,

%T 47764,81542,137356,228363,374755,607213,971675,1536235,2400465,

%U 3708625,5667325,8569742,12827751,19015101,27923781,40638610,58633470,83896398,119089492

%N Molien series for a certain 16-dimensional group of order 20160.

%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.

%o (Magma) K:=Rationals(); M:=MatrixAlgebra(K,4); q1:=DiagonalMatrix(M,[1,-1,1,-1]); p1:=DiagonalMatrix(M,[1,1,-1,-1]); q2:=DiagonalMatrix(M,[1,1,1,-1]); h:=M![1,1,1,1, 1,1,-1,-1, 1,-1,1,-1, 1,-1,-1,1]/2; H:=MatrixGroup<4,K|q1,q2,h,p1>;

%o permstomats:=function(L); n:=#L[1]; M:=MatrixAlgebra(Rationals(),n); a:=#L; MM:=[]; for i in [1..a] do Append(~MM,M ! 0); end for; for i in [1..a] do for j in [1..n] do MM[i][j][L[i][j]]:=1; end for; end for; return MM; end function;

%o MM:=MatrixAlgebra(K,16); hh:=TensorProduct(M ! 1,h); qq1:=TensorProduct(M ! 1,q1); pp1:=TensorProduct(M ! 1,p1); qq2:=TensorProduct(M ! 1,q2);

%o perm:=sub<Sym(16) | (3,5)*(4,6)*(11,13)*(12,14), (3,7)*(4,8)*(11,15)*(12,16), (2,10)*(4,12)*(6,14)*(8,16),(2,9)*(4,11)*(6,13)*(8,15)>; Order(perm);

%o pp:=Setseq(Generators(perm)); L:=[Eltseq(pp[1]),Eltseq(pp[2]),Eltseq(pp[3]),Eltseq(pp[4])]; ML:=permstomats(L); UU:=MatrixGroup<16,K | hh,qq2,ML[1],ML[2],ML[3],ML[4]>; Order(UU); MUU:=MolienSeries(UU);

%K nonn

%O 0,2

%A _N. J. A. Sloane_ and Gabriele Nebe, Apr 26 2005