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The n-Queens Constant.
2

%I #10 Jan 01 2023 08:44:01

%S 1,9,4,4,0,0

%N The n-Queens Constant.

%C Lower bound: 1.944000752019729...

%C Upper bound: 1.9440010813092217...

%H Don Knuth, <a href="https://www-cs-faculty.stanford.edu/~knuth/papers/Xqueens-and-Xqueenons.pdf">Xqueens and Xqueenons</a>, 2021.

%H Parth Nobel, Akshay Agrawal and Stephen Boyd, <a href="https://arxiv.org/abs/2112.03336">Computing tighter bounds on the n-queens constant via Newton’s method</a>, arXiv:2112.03336 [math.CO], 2021.

%H Parth Nobel, Akshay Agrawal and Stephen Boyd, <a href="https://doi.org/10.1007/s11590-022-01933-2">Computing tighter bounds on the n-queens constant via Newton’s method</a>, Sep 17 2022.

%H Michael Simkin, <a href="https://arxiv.org/abs/2107.13460">The number of n-queens configurations</a>, arXiv:2107.13460 [math.CO], 2021.

%H Cheng Zhang and Jianpeng Ma, <a href="http://arxiv.org/abs/0808.4003">Counting Solutions for the N-queens and Latin Square Problems by Efficient Monte Carlo Simulations</a>, arXiv:0808.4003 [cond-mat.stat-mech], 2008.

%F Lim_{n->infinity} A000170(n)^(1/n)/n = exp(-A359441).

%e 1.94400...

%Y Cf. A000170.

%K nonn,cons,hard,more

%O 1,2

%A _Vaclav Kotesovec_, Jan 01 2023