A115223 Number of 3 X 3 symmetric matrices over Z(n) having determinant 0.

1, 36, 261, 1408, 3225, 9396, 17101, 47104, 76545, 116100, 162261, 367488, 373321, 615636, 841725, 1638400, 1424481, 2755620, 2482597, 4540800, 4463361, 5841396, 6447981, 12294144, 11640625, 13439556, 18954729, 24078208, 20534697, 30302100

Offset: 1

Author

T. D. Noe, Jan 16 2006

Keywords

• mult
• nonn

Crossrefs

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

Programs

Mathematica

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}]

Formula

a(n)=n^6-A115225(n). For prime n, a(n)=(n^3+n-1)n^2.