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 A309598 Number of extended self-orthogonal diagonal Latin squares of order n with ordered first string. 0
 1, 0, 0, 2, 4, 0, 256, 4608 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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. LINKS E. I. Vatutin, Discussion about properties of diagonal Latin squares (in Russian) FORMULA From Eduard I. Vatutin, Feb 25 2020: (Start) a(n) = A287761(n) for 1 <= n <= 6. a(n) = 4*A287761(n) for 7 <= n <= 8. (End) 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 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. Sequence in context: A287761 A009512 A317411 * A305570 A287651 A163259 Adjacent sequences:  A309595 A309596 A309597 * A309599 A309600 A309601 KEYWORD nonn,more AUTHOR Eduard I. Vatutin, Aug 09 2019 STATUS approved

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Last modified April 8 08:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)