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A115222 Number of 3 X 3 matrices over Z(n) having nonzero determinant. 2
0, 168, 11232, 161280, 1488000, 7170552, 33784128, 106659840, 327525120, 839997000, 2124276000, 4307378688, 9726417792, 18401146008, 34512588000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A064767 for the number of invertible matrices.

LINKS

Table of n, a(n) for n=1..15.

FORMULA

a(n)=n^9-A115221(n). For prime n, a(n)=A064767(n)=n^3 (n-1)^3 (n+1) (n^2+n+1)

MATHEMATICA

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}]

CROSSREFS

Sequence in context: A019286 A218413 A064767 * A290152 A282586 A035827

Adjacent sequences:  A115219 A115220 A115221 * A115223 A115224 A115225

KEYWORD

nonn

AUTHOR

T. D. Noe, Jan 16 2006

STATUS

approved

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Last modified October 17 02:04 EDT 2019. Contains 328106 sequences. (Running on oeis4.)