A115221 Number of 3 X 3 matrices over Z(n) having determinant 0.

1, 344, 8451, 100864, 465125, 2907144, 6569479, 27557888, 59895369, 160003000, 233671691, 852401664, 878081581, 2259900776, 3930771375

Offset: 1

Author

T. D. Noe, Jan 16 2006

Keywords

• mult
• nonn

Programs

Mathematica

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}]

Formula

a(n)=n^9-A115222(n). For prime n, a(n)=n^3 (n^5+n^4-n^2-n+1)