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

%I #21 Jan 17 2019 18:32:33

%S 0,8,320,43264,22003712,43090149376,326720427917312,

%T 9588057159626653696,1086099857128493963804672

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

%C a(n) = 2^(2n-1)*A046747(n-1). - Kevin Costello, May 18 2005

%H R. P. Brent and J. H. Osborn, <a href="http://arxiv.org/abs/1208.3330">Bounds on minors of binary matrices</a>, arXiv preprint arXiv:1208.3330 [math.CO], 2012. - From _N. J. A. Sloane_, Dec 25 2012

%H Konstantin Tikhomirov, <a href="https://arxiv.org/abs/1812.09016">Singularity of random Bernoulli matrices</a>, arXiv preprint arXiv:1812.09016 [math.PR], 2018-2019.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SingularMatrix.html">Singular Matrix.</a>

%F a(n)/2^(n^2) ~ (1/2 + o_n(1))^n (proved by Tikhomirov). - _Timothy Y. Chow_, Jan 17 2019

%Y Complement of A056990.

%Y Cf. A046747.

%K nonn,more

%O 1,2

%A _Eric W. Weisstein_, Oct 23 2000

%E More terms from Kevin Costello, May 18 2005

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

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Last modified April 19 16:38 EDT 2024. Contains 371794 sequences. (Running on oeis4.)