A387187 a(n) is the number of distinct numbers of transversals in extended self-orthogonal diagonal Latin squares of order n.

1, 0, 0, 1, 1, 0, 4, 5, 244, 62

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 128, 192, 224, 256, or 384. Since there are 3 distinct values, a(8)=5.

Crossrefs

Cf. A309210, A309598, A309599, A344105, A350585, A383684, A387124.

Sequence in context: A041745 A298224 A051152 * A042181 A368531 A042717

Adjacent sequences: A387184 A387185 A387186 * A387188 A387189 A387190

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Aug 21 2025

Status

approved