A389118 a(n) is the number of distinct numbers of diagonal transversals an extended self-orthogonal diagonal Latin square of order n can have.

1, 0, 0, 1, 1, 0, 3, 7, 147, 78

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.

Links

Table of n, a(n) for n=1..10.

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.

Example

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.

Crossrefs

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

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Sep 23 2025

Status

approved