%I A115222
%S A115222 0,168,11232,161280,1488000,7170552,33784128,106659840,327525120,
%T A115222 839997000,2124276000,4307378688,9726417792,18401146008,34512588000
%N A115222 Number of 3 X 3 matrices over Z(n) having nonzero determinant.
%C A115222 See A064767 for the number of invertible matrices.
%F A115222 a(n)=n^9-A115221(n). For prime n, a(n)=A064767(n)=n^3 (n-1)^3 (n+1) (n^2+n+1)
%t A115222 Table[cnt=0; Do[m={{a, b, c}, {d, e, f}, {g, h, i}}; If[Det[m, Modulus->
               n]>0, cnt++ ], {a, 0, n-1}, {b, 0, n-1}, {c, 0, n-1}, {d, 0, n-1}, 
               {e, 0, n-1}, {f, 0, n-1}, {g, 0, n-1}, {h, 0, n-1}, {i, 0, n-1}]; 
               cnt, {n, 2, 7}]
%Y A115222 Sequence in context: A006363 A019286 A064767 this_sequence A035827 A075920 
               A076006
%Y A115222 Adjacent sequences: A115219 A115220 A115221 this_sequence A115223 A115224 
               A115225
%K A115222 nonn
%O A115222 1,2
%A A115222 T. D. Noe (noe(AT)sspectra.com), Jan 16 2006