A329685 Number of main classes of self-orthogonal diagonal Latin squares of order n.

1, 0, 0, 1, 1, 0, 2, 8, 470, 30502

Offset

1,7

Comments

A self-orthogonal diagonal Latin square is a diagonal Latin square orthogonal to its transpose.

A333366(n) <= a(n) <= A309210(n) <= A330391(n). - Eduard I. Vatutin, Apr 26 2020

Links

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

A. D. Belyshev, List of 30502 essentially distinct self-orthogonal diagonal Latin squares of order 10

E. I. Vatutin, Discussion about properties of diagonal Latin squares (in Russian).

E. I. Vatutin, About the number of main classes for SODLS of order 9 (in Russian).

E. I. Vatutin, About the number of SODLS of order 10 (in Russian).

E. I. Vatutin, List of all main classes of 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

Example

0 1 2 3 4 5 6 7 8 9
5 2 0 9 7 8 1 4 6 3
9 5 7 1 8 6 4 3 0 2
7 8 6 4 9 2 5 1 3 0
8 9 5 0 3 4 2 6 7 1
3 6 9 5 2 1 7 0 4 8
4 3 1 7 6 0 8 2 9 5
6 7 8 2 5 3 0 9 1 4
2 0 4 6 1 9 3 8 5 7
1 4 3 8 0 7 9 5 2 6

Crossrefs

Cf. A309210, A287761, A287762.

Sequence in context: A009808 A035129 A284603 * A323863 A003301 A000890

Adjacent sequences: A329682 A329683 A329684 * A329686 A329687 A329688

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Feb 25 2020

Extensions

a(9) from Eduard I. Vatutin, Mar 12 2020

a(10) from Eduard I. Vatutin, Mar 14 2020

a(10) corrected by Natalia Makarova, Apr 10 2020

Status

approved