OFFSET
1,7
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
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.
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)
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Eduard I. Vatutin, Nov 10 2021
STATUS
approved