A350025 Number of totally symmetric Latin squares of order n.

1, 2, 3, 16, 30, 480, 1290, 163200, 471240, 386400000, 2269270080, 12238171545600, 149648961369600, 8089070513113497600, 160650421233958656000, 91361407076595590705971200

Offset: 1

Author

Ian Wanless, Dec 08 2021

Keywords

• nonn
• more

Comments

A Latin square is "totally symmetric" if all 6 of its conjugates are equal.

Links

• 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. A076019, A350026.

Extensions

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