A354050 a(n) is the number of distinct numbers of intercalates that an orthogonal diagonal Latin square of order n can have.

0, 0, 0, 1, 1, 0, 3, 26, 55

Offset: 1

Author

Eduard I. Vatutin, May 16 2022

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) <= A345760(n).

a(10) >= 74, a(11) >= 76, a(12) >= 190. - updated by Eduard I. Vatutin, Mar 01 2025

Examples

			For n=8 the number of intercalates that an orthogonal diagonal Latin square of order 8 may have is 2, 4, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 36, 40, 44, 48, 52, 56, 64, 80, or 112. Since there are 26 distinct values, a(8)=26.
		

Links

• Eduard I. Vatutin, About the spectra of numerical characteristics of orthogonal diagonal Latin squares of orders 1-11 (in Russian).
• 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)
• E. I. Vatutin, V. S. Titov, A. I. Pykhtin, A. V. Kripachev, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan and I. I. Kurochkin, Estimation of the Cardinalities of the Spectra of Fast-computable Numerical Characteristics for Diagonal Latin Squares of Orders N>9 (in Russian) // Science and education in the development of industrial, social and economic spheres of Russian regions. Murom, 2022. pp. 314-315.
• Eduard I. Vatutin, Graphical representation of the spectra.
• Eduard I. Vatutin, Proving lists (4, 5, 7, 8, 9, 10, 11, 12).
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A345760, A349199, A350585.