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

Author

Eduard I. Vatutin, Apr 10 2025

Keywords

• nonn
• more
• hard
• changed

Comments

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.

Examples

			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.
		

Links

• 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.

Crossrefs

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