A076021 Number of fully idempotent systems with n elements with one binary operation satisfying the equation B(AB)=A (idempotent semisymmetric quasigroups).

1, 0, 1, 1, 0, 0, 4, 0, 20, 241, 0, 9801188

Offset: 1

Author

Richard C. Schroeppel, Oct 29 2002

Keywords

• nonn
• hard
• more

Comments

a(n) = 0 whenever n == 2 (mod 3).

a(n) is also the number of unipotent semisymmetric quasigroups of order n+1 and is also the number of semisymmetric loops of order n+1.

Links

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

Crossrefs

Cf. A076016-A076020.

Extensions

a(10)-a(12) from Ian Wanless, Dec 08 2021