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A005353 Number of 2 X 2 matrices with entries mod n and nonzero determinant.
(Formerly M4254)
5
0, 6, 48, 168, 480, 966, 2016, 3360, 5616, 8550, 13200, 17832, 26208, 34566, 45840, 59520, 78336, 95526, 123120, 147240, 181776, 219846, 267168, 307488, 372000, 433446, 505440, 580776, 682080, 762150, 892800, 999936, 1138368, 1284486 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

T. Brenner, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

R. K. Guy, Letter to N. J. A. Sloane, Sep 1989

FORMULA

a(n) = n^4 - A020478(n).

For prime n, a(n) = (n^2-1)(n-1)n. - T. D. Noe, Jan 12 2006

MATHEMATICA

Table[cnt=0; Do[m={{a, b}, {c, d}}; If[Det[m, Modulus->p] > 0, cnt++ ], {a, 0, p-1}, {b, 0, p-1}, {c, 0, p-1}, {d, 0, p-1}]; cnt, {p, 37}] (* T. D. Noe, Jan 12 2006 *)

CROSSREFS

Cf. A059306, A062801.

Sequence in context: A244726 A335384 A331668 * A047927 A059238 A254832

Adjacent sequences:  A005350 A005351 A005352 * A005354 A005355 A005356

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, R. K. Guy

EXTENSIONS

More terms from T. D. Noe, Jan 12 2006

STATUS

approved

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Last modified May 10 05:05 EDT 2021. Contains 343748 sequences. (Running on oeis4.)