A382505 a(n) is the number of distinct numbers of diagonal transversals in Brown's diagonal Latin squares of order 2n.

0, 1, 2, 20, 349

Offset: 1

Author

Eduard I. Vatutin, Mar 29 2025

Keywords

• nonn
• more
• hard

Comments

A Brown's diagonal Latin square is a horizontally symmetric row-inverse or vertically symmetric column-inverse diagonal Latin square (see A339641).

Brown's diagonal Latin squares are special case of plain symmetry diagonal Latin squares that do not exist for odd orders.

a(6)>=1785, a(7)>=60341, a(8)>=4151.

Examples

			For n=4 the number of transversals that a diagonal Latin square of order 8 may have is 0, 8, 12, 16, 18, 20, 24, 26, 28, 32, 36, 40, 44, 48, 52, 56, 64, 88, 96, or 120. Since there are 20 distinct values, a(4)=20.
		

Links

• Eduard I. Vatutin, About the spectra of numerical characteristics of Brown's diagonal Latin squares (in Russian).
• Eduard I. Vatutin, Proving lists (4, 6, 8, 10).
• Eduard I. Vatutin, Graphical representation of the spectra.
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A339641, A344105, A381971.