A002884 - OEIS

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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)

1, 1, 6, 168, 20160, 9999360, 20158709760, 163849992929280, 5348063769211699200, 699612310033197642547200, 366440137299948128422802227200, 768105432118265670534631586896281600 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	`Also number of bases for GF(2^n) over GF(2).` `Also (apparently) number of n X n matrices over GF(2) having permanent = 1. [Hugo Pfoertner, Nov 14 2003]. This is true because over GF(2) permanents and determinants are the same. [Joerg Arndt, Mar 07 2008]`
	REFERENCES	`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.` `Dai, Zong Duo; Golomb, Solomon W.; and Gong, Guang, Generating all linear orthomorphisms without repetition. Discrete Math. 205 (1999), 47-55.` `P. F. Duvall, Jr. and P. W. Harley, III, A note on counting matrices, SIAM J. Appl. Math., 20 (1971), 374-377.` `Horadam, K. J., Hadamard matrices and their applications. Princeton University Press, Princeton, NJ, 2007. xiv+263 pp. See p. 132.` `Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.` `N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).` `N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).` `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 to divisibility sequences` `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).` `a(n) = A203303(n+1)/A203303(n). - R. J. Mathar, Jan 06 2012`
	MAPLE	`product(2^n-2^i, i=0..n-1); or 2^(n(n-1)/2) product( 2^i - 1, i=1..n);`
	MATHEMATICA	`Table[Product[2^n-2^i, {i, 0, n-1}], {n, 0, 13}] (* From Harvey P. Dale, Aug 07 2011 *)`
	PROG	`(PARI) a(n)=prod(i=2, n, 2^i-1)<<binomial(n, 2) \\ Charles R Greathouse IV, Jan 13 2012`
	CROSSREFS	`Cf. A000409, A000410, A002820, A046747, A048651.` `Sequence in context: A106661 A181013 A003720 * A198176 A166762 A055165` `Adjacent sequences: A002881 A002882 A002883 * A002885 A002886 A002887`
	KEYWORD	`nonn,easy,nice,changed`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com).`

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Last modified February 14 11:36 EST 2012. Contains 205623 sequences.