A349199 a(n) is the number of distinct numbers of diagonal transversals that an orthogonal diagonal Latin square of order n can have.

1, 0, 0, 1, 1, 0, 3, 31, 165

Offset: 1

Author

Eduard I. Vatutin, Nov 10 2021

Keywords

• nonn
• more
• hard

Comments

An orthogonal diagonal Latin square is a diagonal Latin square with at least one orthogonal diagonal mate. Since all orthogonal diagonal Latin squares are diagonal Latin squares, a(n) <= A345370(n).

a(10) >= 390, a(11) >= 560, a(12) >= 13429. - Eduard I. Vatutin, Nov 10 2021, updated Jan 29 2023

Examples

			For n=8 the number of diagonal transversals that an orthogonal diagonal Latin square of order 8 may have is 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 28, 30, 32, 36, 38, 40, 42, 44, 48, 52, 56, 64, 72, 88, 96, or 120. Since there are 31 distinct values, a(8)=31.
		

Links

• Eduard I. Vatutin, About the spectra of numerical characteristics of orthogonal diagonal Latin squares of orders 1-11 (in Russian).
• Eduard I. Vatutin, Graphical representation of the spectra.
• Eduard I. Vatutin, Proving lists (1, 4, 5, 7, 8, 9, 10, 11, 12).
• E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan and I. I. Kurochkin, On the construction of spectra of fast-computable numerical characteristics for diagonal Latin squares of small order, Intellectual and Information Systems (Intellect - 2021). Tula, 2021. pp. 7-17. (in Russian)
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A305570, A345370.