1,2

See A064767 for the number of invertible matrices.

a(n)=n^9-A115221(n). For prime n, a(n)=A064767(n)=n^3 (n-1)^3 (n+1) (n^2+n+1)

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}]

Sequence in context: A006363 A019286 A064767 this_sequence A035827 A075920 A076006

Adjacent sequences: A115219 A115220 A115221 this_sequence A115223 A115224 A115225

nonn

T. D. Noe (noe(AT)sspectra.com), Jan 16 2006