A115222 - OEIS

%I #3 Mar 30 2012 17:22:41

%S 0,168,11232,161280,1488000,7170552,33784128,106659840,327525120,

%T 839997000,2124276000,4307378688,9726417792,18401146008,34512588000

%N Number of 3 X 3 matrices over Z(n) having nonzero determinant.

%C See A064767 for the number of invertible matrices.

%F 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 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}]

%K nonn

%O 1,2

%A _T. D. Noe_, Jan 16 2006