A076016 Number of systems with n elements having one binary operation satisfying the equation B(AB)=A (semisymmetric quasigroups).

1, 2, 3, 18, 120, 2880, 140256, 20782080, 9569532672, 14175610675200, 74559788174868480

Offset: 1

Author

Richard C. Schroeppel, Oct 29 2002

Keywords

• nonn
• hard
• more

Comments

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

Links

• Brendan D. McKay and Ian M. Wanless, Enumeration of Latin squares with conjugate symmetry, J. Combin. Des. 30 (2022), 105-130.

Crossrefs

Cf. A076017-A076021, A350019, A350020.

Extensions

a(10)-a(11) from Ian Wanless, Dec 08 2021