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A057982
Number of singular n X n (-1,1)-matrices.
1
0, 8, 320, 43264, 22003712, 43090149376, 326720427917312, 9588057159626653696, 1086099857128493963804672
OFFSET
1,2
COMMENTS
a(n) = 2^(2n-1)*A046747(n-1). - Kevin Costello, May 18 2005
LINKS
R. P. Brent and J. H. Osborn, Bounds on minors of binary matrices, arXiv preprint arXiv:1208.3330 [math.CO], 2012. - From N. J. A. Sloane, Dec 25 2012
Konstantin Tikhomirov, Singularity of random Bernoulli matrices, arXiv preprint arXiv:1812.09016 [math.PR], 2018-2019.
Eric Weisstein's World of Mathematics, Singular Matrix.
FORMULA
a(n)/2^(n^2) ~ (1/2 + o_n(1))^n (proved by Tikhomirov). - Timothy Y. Chow, Jan 17 2019
CROSSREFS
Complement of A056990.
Cf. A046747.
Sequence in context: A282621 A300189 A227657 * A308615 A041769 A209277
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, Oct 23 2000
EXTENSIONS
More terms from Kevin Costello, May 18 2005
a(6)-a(9) from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 18 2008
STATUS
approved