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A002884 Number of nonsingular n X n matrices over GF(2) (order of Chevalley group A_n (2)).
(Formerly M4302 N1798)
+0
32
1, 1, 6, 168, 20160, 9999360, 20158709760, 163849992929280, 5348063769211699200, 699612310033197642547200, 366440137299948128422802227200, 768105432118265670534631586896281600 (list; graph; listen)
OFFSET

0,3

COMMENT

Also (apparently) number of n X n matrices over GF(2) having permanent = 1. - Hugo Pfoertner (hugo(AT) pfoertner.org), Nov 14 2003. This is true because over GF(2) permanents and determinants are the same! - Joerg Arndt (arndt(AT)jjj.de), Mar 07 2008

REFERENCES

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985, p. xvi.

H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.

P. F. Duvall, Jr. and P. W. Harley, III, A note on counting matrices, SIAM J. Appl. Math., 20 (1971), 374-377.

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.

LINKS

T. D. Noe, Table of n, a(n) for n=0..30

J. Overbey, W. Traves and J. Wojdylo, On the Keyspace of the Hill Cipher

Index entries for sequences related to binary matrices

FORMULA

Product(2^n-2^i, i=0..n-1); or 2^(n*(n-1)/2) * product( 2^i - 1, i=1..n).

MAPLE

product(2^n-2^i, i=0..n-1); or 2^(n*(n-1)/2) * product( 2^i - 1, i=1..n);

CROSSREFS

Cf. A000409, A000410, A002820, A046747, A048651.

Adjacent sequences: A002881 A002882 A002883 this_sequence A002885 A002886 A002887

Sequence in context: A104729 A106661 A003720 this_sequence A166762 A055165 A071095

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified November 7 16:45 EST 2009. Contains 166093 sequences.


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