A076016 - OEIS

%I #14 Dec 09 2021 00:47:05

%S 1,2,3,18,120,2880,140256,20782080,9569532672,14175610675200,

%T 74559788174868480

%N Number of systems with n elements having one binary operation satisfying the equation B(AB)=A (semisymmetric quasigroups).

%C Or, Latin squares for which the set of (row,column,symbol) triples is invariant under cyclic permutation of the elements within each triple.

%H Brendan D. McKay and Ian M. Wanless, <a href="https://doi.org/10.1002/jcd.21814">Enumeration of Latin squares with conjugate symmetry</a>, J. Combin. Des. 30 (2022), 105-130.

%Y Cf. A076017-A076021, A350019, A350020.

%K nonn,hard,more

%O 1,2

%A Richard C. Schroeppel, Oct 29 2002

%E a(10)-a(11) from _Ian Wanless_, Dec 08 2021