A076019 Number of nonisomorphic commutative systems with n elements with one binary operation satisfying the equation B(AB)=A (totally-symmetric quasigroups).

1, 1, 2, 2, 1, 3, 3, 13, 12, 139, 65, 25894, 24316, 92798256, 122859802, 4366600209354

Offset

1,3

Links

Table of n, a(n) for n=1..16.

Hy Ginsberg, Totally Symmetric Quasigroups of Order 16, arXiv preprint (2022). arXiv:2211.13204 [math.CO]

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

Crossrefs

Cf. A076016-A076021.

Sequence in context: A372688 A011020 A181512 * A071453 A212306 A339708

Adjacent sequences: A076016 A076017 A076018 * A076020 A076021 A076022

Keyword

nonn,hard,more

Author

Richard C. Schroeppel, Oct 29 2002

Extensions

a(10)-a(15) from Ian Wanless, Dec 08 2021

a(16) from Ginsberg link via Charles R Greathouse IV, Dec 02 2022

Status

approved