A381626 Number of horizontal plane Brown's diagonal Latin squares of order 2n.

0, 48, 92160, 1981808640, 1735113100492800

Offset: 1

Author

Eduard I. Vatutin, Mar 02 2025

Keywords

• nonn
• more
• hard

Comments

Brown's diagonal Latin square is a horizontally symmetric row-inverse (horizontal plane Brown's diagonal Latin square) or vertically symmetric column-inverse diagonal Latin square (vertical plane Brown's diagonal Latin square). Diagonal Latin squares of this type have interesting properties, for example, a large number of transversals.

Also number of vertical plane Brown's diagonal Latin squares of order 2n with the first row in order.

Plain symmetry diagonal Latin squares do not exist for odd orders.

Links

• E. I. Vatutin, Special types of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022), Pereslavl-Zalessky, 2023, pp. 9-18 (in Russian).
• Eduard I. Vatutin, Enumeration of the Brown's diagonal Latin squares of orders 1-9 (in Russian).
• Eduard I. Vatutin, Clarification for Brown's diagonal Latin squares for orders 6 and 8 (in Russian).
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A292516, A339641, A340186, A379145.

Formula

a(n) = A379145(n) * (2n)!.

Extensions

a(5) added by Oleg S. Zaikin and Eduard I. Vatutin, Apr 08 2025