%I #32 Mar 16 2023 10:28:24

%S 1,1,1,12,192,145164,1524901344

%N Number of structurally distinct Latin squares of order n.

%C "Structurally distinct" means that the squares cannot be made identical by means of rotation, reflection, and/or permutation of the symbols. For other notions of distinctness, see A000479 and A040082.

%D Hendrik Willem Barink, Email to N. J. A. Sloane, Nov 22 2015

%H Hendrik Willem Barink, <a href="http://www.latinsquares5x5.wordpress.com">How many structurally different latin squares do exist?</a>

%H Gabriel Crudele, Peter Dukes, and Jonathan A. Noel, <a href="https://arxiv.org/abs/2303.04776">Six Permutation Patterns Force Quasirandomness</a>, arXiv:2303.04776 [math.CO], 2023.

%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/q/1381193">How many structurally different latin squares of order 5 exist?</a>

%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/q/2143780">How many structurally distinct Latin squares are there of order 7?</a>

%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>

%Y Cf. A000479, A040082.

%K nonn,more

%O 1,4

%A _N. J. A. Sloane_, Nov 23 2015

%E a(7) from MSE link, added by _Max Alekseyev_, Sep 01 2017