A379145 Number of horizontal plane Brown's diagonal Latin squares of order 2n with the first row in order.

0, 2, 64, 49152, 478150656

Offset

1,2

Comments

A 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

Table of n, a(n) for n=1..5.

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.

Formula

a(n) = A381626(n) / (2n)!.

Crossrefs

Cf. A287649, A339305, A339641, A340186, A381626.

Sequence in context: A085535 A060613 A139772 * A348214 A092238 A228252

Adjacent sequences: A379142 A379143 A379144 * A379146 A379147 A379148

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Dec 16 2024

Extensions

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

Status

approved