1,7

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

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.

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.

Cf. A345760, A349199, A350585.

Sequence in context: A358352 A083109 A191590 * A177511 A387659 A294494

Adjacent sequences: A354047 A354048 A354049 * A354051 A354052 A354053

nonn,more,hard

Eduard I. Vatutin, May 16 2022

approved