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A349199
a(n) is the number of distinct numbers of diagonal transversals that an orthogonal diagonal Latin square of order n can have.
5
1, 0, 0, 1, 1, 0, 3, 31, 165
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, 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)
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
Sequence in context: A089286 A089287 A125085 * A007233 A197892 A198009
KEYWORD
nonn,more,hard
AUTHOR
Eduard I. Vatutin, Nov 10 2021
STATUS
approved