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A115225 Number of 3 X 3 symmetric matrices over Z(n) having nonzero determinant. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 7 10:30 EST 2021. Contains 341869 sequences. (Running on oeis4.)