A387124 -id:A387124 - cp's OEIS frontend

A383684 Minimum number of transversals in an extended self-orthogonal diagonal Latin square of order n.

1, 0, 0, 8, 15, 0, 23, 128, 133, 716

Offset: 1

Eduard I. Vatutin, May 05 2025

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 list (best known examples).
Index entries for sequences related to Latin squares and rectangles.

Cf. A090741, A091323, A287644, A287645, A309210, A309598, A309599, A357514, A387124, A387187.

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

Original entry on oeis.org

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

Offset: 1

Eduard I. Vatutin, Aug 21 2025

			For n=8 the number of transversals that an extended self-orthogonal diagonal Latin square of order 7 may have is 128, 192, 224, 256, or 384. Since there are 3 distinct values, a(8)=5.

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.

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

cp's OEIS Frontend

A383684 Minimum number of transversals in an extended self-orthogonal diagonal Latin square of order n.

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