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

1,2

Links

Table of n, a(n) for n=1..30.

Formula

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

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}]

Crossrefs

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

Sequence in context: A341544 A115332 A133072 * A135181 A220159 A202958

Adjacent sequences: A115220 A115221 A115222 * A115224 A115225 A115226

Keyword

mult,nonn

Author

T. D. Noe, Jan 16 2006

Status

approved