1,7

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.

Eduard I. Vatutin, About the properties of ESODLS of orders 1-10 (in Russian).

Eduard I. Vatutin, Proving lists (1, 4, 5, 7, 8, 9, 10).

Eduard I. Vatutin, Graphical representation of the spectra.

Index entries for sequences related to Latin squares and rectangles.

For n=8 the number of transversals that an extended self-orthogonal diagonal Latin square of order 8 may have is 16, 24, 32, 40, 48, 56, or 96. Since there are 7 distinct values, a(8)=7.

Cf. A309210, A309598, A309599, A345370, A349199, A387236, A387360.

Sequence in context: A012636 A006031 A219166 * A374090 A119958 A275195

Adjacent sequences: A389115 A389116 A389117 * A389119 A389120 A389121

nonn,more,hard

Eduard I. Vatutin, Sep 23 2025

approved