A057982 Number of singular n X n (-1,1)-matrices.

0, 8, 320, 43264, 22003712, 43090149376, 326720427917312, 9588057159626653696, 1086099857128493963804672

Offset: 1

Author

Eric W. Weisstein, Oct 23 2000

Keywords

• nonn
• more

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.

Crossrefs

Complement of A056990.

Cf. A046747.

Formula

a(n)/2^(n^2) ~ (1/2 + o_n(1))^n (proved by Tikhomirov). - Timothy Y. Chow, Jan 17 2019

Extensions

More terms from Kevin Costello, May 18 2005

a(6)-a(9) from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 18 2008