OFFSET

1,4

COMMENTS

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

LINKS

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

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

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.

FORMULA

a(n) = A287761(n)*n!.

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

KEYWORD

nonn,more,hard

AUTHOR

Eduard I. Vatutin, May 31 2017

EXTENSIONS

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

a(10) corrected by Eduard I. Vatutin, Apr 24 2020

STATUS

approved