A382952 -id:A382952 - cp's OEIS frontend

A382957 a(n) is the number of distinct numbers of intercalates in an extended self-orthogonal diagonal Latin squares of order n.

1, 0, 0, 1, 1, 0, 3, 8, 52, 45

Offset: 1

Eduard I. Vatutin, Apr 10 2025

A self-orthogonal diagonal Latin square (SODLS, see A329685) is a diagonal Latin square orthogonal to its transpose. An extended self-orthogonal diagonal Latin square (ESODLS, see A309210) is a diagonal Latin square that has an orthogonal diagonal Latin square from the same main class. SODLS is a special case of ESODLS.

			For n=7 the number of intercalates that an extended self-orthogonal diagonal Latin square of order 7 may have is 0, 10, or 18. Since there are 3 distinct values, a(7)=3.

Eduard I. Vatutin, Proving lists (1, 4, 5, 7, 8, 9, 10).
Eduard I. Vatutin, Graphical representation of the spectra.
Eduard I. Vatutin, About the properties of ESODLS of orders 1-10 (in Russian).
Index entries for sequences related to Latin squares and rectangles.

Cf. A309210, A309598, A309599, A329685, A345760, A382952.

cp's OEIS Frontend

A382957 a(n) is the number of distinct numbers of intercalates in an extended self-orthogonal diagonal Latin squares of order n.

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