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 A309210 Number of main classes of extended self-orthogonal diagonal Latin squares of order n. 3
 1, 0, 0, 1, 1, 0, 5, 23 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS A self-orthogonal diagonal Latin square (SODLS) is a diagonal Latin square orthogonal to its transpose. An extended self-orthogonal diagonal Latin square (ESODLS) is a diagonal Latin square that has an orthogonal diagonal Latin square from the same main class. SODLS is a special case of ESODLS. A333366(n) <= A329685(n) <= a(n) <= A330391(n). - Eduard I. Vatutin, Jun 07 2020 a(10) >= 33240. - Eduard I. Vatutin, Jul 09 2020 LINKS E. I. Vatutin, Discussion about properties of diagonal Latin squares (in Russian) E. I. Vatutin, About the lower bound of number of ESODLS of order 10 (in RUssian). EXAMPLE The diagonal Latin square   0 1 2 3 4 5 6 7 8 9   1 2 0 4 5 7 9 8 6 3   5 0 1 6 3 9 8 2 4 7   9 3 5 8 2 1 7 4 0 6   4 6 3 5 7 8 0 9 2 1   8 4 6 9 1 3 2 5 7 0   7 8 9 0 6 4 5 1 3 2   2 9 4 7 8 0 3 6 1 5   6 5 7 1 0 2 4 3 9 8   3 7 8 2 9 6 1 0 5 4 has the orthogonal diagonal Latin square   0 1 2 3 4 5 6 7 8 9   3 5 9 8 6 2 0 1 4 7   4 3 8 7 2 1 9 0 5 6   6 9 3 4 8 0 1 2 7 5   7 2 0 1 9 3 5 8 6 4   2 0 1 5 7 6 4 9 3 8   8 6 4 2 0 9 7 5 1 3   1 7 6 0 5 4 8 3 9 2   9 8 5 6 1 7 3 4 2 0   5 4 7 9 3 8 2 6 0 1 from the same main class. CROSSREFS Cf. A287761, A333366, A329685, A330391. Sequence in context: A002069 A298233 A215742 * A282688 A282875 A317679 Adjacent sequences:  A309207 A309208 A309209 * A309211 A309212 A309213 KEYWORD nonn,more AUTHOR Eduard I. Vatutin, Aug 09 2019 STATUS approved

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Last modified September 20 04:43 EDT 2020. Contains 337264 sequences. (Running on oeis4.)