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

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

1,2

Links

Table of n, a(n) for n=1..27.

Formula

a(n)=n^6-A115223(n). For prime n, a(n)=(n^3-1)(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. A115222 (number of 3 X 3 matrices over Z(n) having nonzero determinant).

Sequence in context: A160060 A115226 A086782 * A223997 A263949 A240463

Adjacent sequences: A115222 A115223 A115224 * A115226 A115227 A115228

Keyword

nonn

Author

T. D. Noe, Jan 16 2006

Status

approved