A115222 -id:A115222 - cp's OEIS frontend

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

T. D. Noe, Jan 16 2006

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}]

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

A115225 Number of 3 X 3 symmetric matrices over Z(n) having nonzero determinant.

Original entry on oeis.org

0, 28, 468, 2688, 12400, 37260, 100548, 215040, 454896, 883900, 1609300, 2618496, 4453488, 6913900, 10548900, 15138816, 22713088, 31256604, 44563284, 59459200, 81302760, 107538508, 141587908, 178808832, 232500000, 295476220, 368465760

Offset: 1

T. D. Noe, Jan 16 2006

nonn

Cf. A115222 (number of 3 X 3 matrices over Z(n) having nonzero determinant).

Table[cnt=0; Do[m={{a, b, c}, {b, d, e}, {c, e, f}}; 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}]; cnt, {n, 2, 20}]

a(n)=n^6-A115223(n). For prime n, a(n)=(n^3-1)(n-1)n^2.

cp's OEIS Frontend

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

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