0,4

Index entries for Molien series

G.f.: (x^36+x^28+x^26+x^24+2*x^20+2*x^16+x^12+x^10+x^8+1) / ((x^2-1)*(x^6-1)*(x^8-1)*(x^24-1)).

1 + x^2 + x^4 + 2*x^6 + 4*x^8 + 5*x^10 + 7*x^12 + ...

(MAGMA) // Definition of group:

F<al> := CyclotomicField(24); i := al^6; eta := al^3; s2 := (1+i)/eta; om := al^8; s3 := (2*om+1)/i; s6 := s2*s3; M := GeneralLinearGroup(4, F);

A1 := M![s3/s6, 1/s6, 1/s6, 1/s6, -1/s6, s3/s6, -1/s6, 1/s6, -1/s6, 1/s6, s3/s6, -1/s6, -1/s6, -1/s6, 1/s6, s3/s6 ]; A2 := M![0, 1/s3, 1/s3, 1/s3, -1/s3, 0, -1/s3, 1/s3, -1/s3, 1/s3, 0, -1/s3, -1/s3, -1/s3, 1/s3, 0 ];

B1 := M![ -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1 ]; C1 := M![1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0 ];

C2 := M![0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0 ]; G := sub<M | A1, A2, B1, C1, C2 >;

The group in A078411 is a subgroup.

Sequence in context: A056833 A105771 A161832 this_sequence A056908 A060565 A133254

Adjacent sequences: A078401 A078402 A078403 this_sequence A078405 A078406 A078407

nonn

N. J. A. Sloane (njas(AT)research.att.com), Dec 27 2002