A333366 Number of main classes of doubly self-orthogonal diagonal Latin squares of order n.

1, 0, 0, 1, 1, 0, 2, 8, 88, 0

Offset: 1

Author

Eduard I. Vatutin, Mar 17 2020

Keywords

• nonn
• more
• hard

Comments

A doubly self-orthogonal diagonal Latin square (DSODLS) is a diagonal Latin square orthogonal to its transpose and antitranspose.

a(n) <= A329685(n) <= A309210(n) <= A330391(n). - Eduard I. Vatutin, Jun 01 2020

Examples

			0 1 2 3 4 5 6 7 8
2 4 3 0 7 6 8 1 5
4 6 7 1 8 2 3 5 0
8 3 5 6 0 7 1 2 4
7 8 1 4 5 3 0 6 2
3 7 0 2 1 8 5 4 6
1 5 4 7 6 0 2 8 3
5 0 6 8 2 1 4 3 7
6 2 8 5 3 4 7 0 1
		

Links

• R. Lu, S. Liu, and J. Zhang, Searching for Doubly Self-orthogonal Latin Squares. Lecture Notes in Computer Science 6876 (2011), 538-545.
• E. I. Vatutin, About the number of DSODLS of orders 1-10 (in Russian).
• E. I. Vatutin, List of all main classes of doubly self-orthogonal diagonal Latin squares of orders 1-10.
• E. I. Vatutin, Special types of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 9-18. (in Russian)
• E. I. Vatutin and A. D. Belyshev, About the number of self-orthogonal (SODLS) and doubly self-orthogonal diagonal Latin squares (DSODLS) of orders 1-10. High-performance computing systems and technologies. Vol. 4. No. 1. 2020. pp. 58-63. (in Russian)
• E. Vatutin and A. Belyshev, Enumerating the Orthogonal Diagonal Latin Squares of Small Order for Different Types of Orthogonality, Communications in Computer and Information Science, Vol. 1331, Springer, 2020, pp. 586-597.
• Eduard I. Vatutin, Natalia N. Nikitina, and Maxim O. Manzuk, First results of an experiment on studying the properties of DLS of order 9 in the volunteer distributed computing projects Gerasim@Home and RakeSearch (in Russian).
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A329685, A309210, A333367.

Extensions

a(10) = 0 is established by Lu et al. (2011).