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Search: id:A005353
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| A005353 |
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Number of 2 X 2 matrices with entries mod n and nonzero determinant.
(Formerly M4254)
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+0
4
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| 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; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
T. Brenner, personal communication.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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a(n) = n^4 - A020478(n).
For prime n, a(n)=(n^2-1)(n-1)n - T. D. Noe (noe(AT)sspectra.com), Jan 12 2006
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MATHEMATICA
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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}] (Noe)
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CROSSREFS
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Cf. A059306, A062801.
Sequence in context: A052651 A153796 A167547 this_sequence A047927 A059238 A026695
Adjacent sequences: A005350 A005351 A005352 this_sequence A005354 A005355 A005356
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Jan 12 2006
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