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A350585
a(n) is the number of distinct numbers of transversals that an orthogonal diagonal Latin square of order n can have.
3
1, 0, 0, 1, 1, 0, 4, 25, 295
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) <= A344105(n).
a(10) >= 193, a(11) >= 3588, a(12) >= 10465. - updated by Eduard I. Vatutin, Jan 29 2023
LINKS
Eduard I. Vatutin, Examples (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 transversals that an orthogonal diagonal Latin square of order 8 may have is 16, 32, 40, 48, 52, 56, 60, 64, 68, 72, 76, 80, 88, 96, 112, 128, 132, 144, 160, 168, 192, 224, 256, 320, or 384. Since there are 25 distinct values, a(8)=25.
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Eduard I. Vatutin, Mar 27 2022
STATUS
approved