Search: id:A068491
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%I A068491
%S A068491 1,1,2,3,6,8,13,17,25,31,42,52,68,81,101,119,145,168,200,229,268,303,349,
%T A068491 392,447,497,560,619,692,760,843,921,1015,1103,1208,1308,1426,1537,1667,
%U A068491 1791,1935,2072,2230,2381,2554,2719,2907,3088,3293,3489,3710,3923,4162
%N A068491 Expansion of Molien series for certain 4-D group of order 96.
%H A068491 <a href="Sindx_Mo.html#Molien">Index entries for Molien series</a>
%F A068491 G.f.: (x^22+x^16+x^14+x^12+x^10+x^8+x^6+1)/((1-x^2)*(1-x^4)*(1-x^8)*(1-x^12)).
%e A068491 1 + x^2 + 2*x^4 + 3*x^6 + 6*x^8 + 8*x^10 + 13*x^12 + 17*x^14 + 25*x^16 
               + 31*x^18 + ...
%o A068491 (MAGMA) // Definition of group: F<al> := CyclotomicField(12); w := al^4; 
               i := al^3; s3 := (1+2*w)/i; M := GeneralLinearGroup(4, F);
%o A068491 g1 := M![ 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0 ]; g2 := M![ 
               -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ]; g3 := M![ 0, 1, 
               0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,-1 ];
%o A068491 H := 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 ]; G := sub<M| g1,g2,g3,H>;
%Y A068491 Sequence in context: A101136 A036957 A022943 this_sequence A024788 A004101 
               A003405
%Y A068491 Adjacent sequences: A068488 A068489 A068490 this_sequence A068492 A068493 
               A068494
%K A068491 nonn
%O A068491 0,3
%A A068491 N. J. A. Sloane (njas(AT)research.att.com), Dec 31 2002

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