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

1,2

Comments

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

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. A076019, A350026.

Sequence in context: A302837 A034382 A034383 * A072684 A344747 A073633

Adjacent sequences: A350022 A350023 A350024 * A350026 A350027 A350028

Keyword

nonn,more

Author

Ian Wanless, Dec 08 2021

Extensions

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

Status

approved