A287762 Number of self-orthogonal diagonal Latin squares of order n.

1, 0, 0, 48, 480, 0, 322560, 46448640, 81587036160, 850065850368000

Offset

1,4

Comments

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

A333671(n) <= a(n) <= A309599(n) <= A305571(n). - Eduard I. Vatutin, Apr 26 2020.

Links

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

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, 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.

H. White, Self-orthogonal Diagonal Latin Squares. How many.

Index entries for sequences related to Latin squares and rectangles.

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

Cf. A160368, A287761, A329685.

Sequence in context: A259851 A223419 A333671 * A309599 A305571 A229505

Adjacent sequences: A287759 A287760 A287761 * A287763 A287764 A287765

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