A309599 Number of extended self-orthogonal diagonal Latin squares of order n.

1, 0, 0, 48, 480, 0, 1290240, 185794560

Offset

1,4

Comments

A self-orthogonal diagonal Latin square (SODLS) is a diagonal Latin square orthogonal to its transpose. An extended self-orthogonal diagonal Latin square (ESODLS) is a diagonal Latin square that has an orthogonal diagonal Latin square from the same main class. SODLS is a special case of ESODLS.

A333671(n) <= A287762(n) <= a(n) <= A305571(n). - Eduard I. Vatutin, Jun 07 2020

a(10) >= 1852743352320000. - Eduard I. Vatutin, Jul 10 2020

Links

Table of n, a(n) for n=1..8.

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

E. I. Vatutin, About the lower bound of number of ESODLS of order 10 (in Russian).

E. I. Vatutin, List of all main classes of extended self-orthogonal diagonal Latin squares of orders 1-8.

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.

Index entries for sequences related to Latin squares and rectangles

Example

The diagonal Latin square
  0 1 2 3 4 5 6 7 8 9
  1 2 0 4 5 7 9 8 6 3
  5 0 1 6 3 9 8 2 4 7
  9 3 5 8 2 1 7 4 0 6
  4 6 3 5 7 8 0 9 2 1
  8 4 6 9 1 3 2 5 7 0
  7 8 9 0 6 4 5 1 3 2
  2 9 4 7 8 0 3 6 1 5
  6 5 7 1 0 2 4 3 9 8
  3 7 8 2 9 6 1 0 5 4
has orthogonal diagonal Latin square
  0 1 2 3 4 5 6 7 8 9
  3 5 9 8 6 2 0 1 4 7
  4 3 8 7 2 1 9 0 5 6
  6 9 3 4 8 0 1 2 7 5
  7 2 0 1 9 3 5 8 6 4
  2 0 1 5 7 6 4 9 3 8
  8 6 4 2 0 9 7 5 1 3
  1 7 6 0 5 4 8 3 9 2
  9 8 5 6 1 7 3 4 2 0
  5 4 7 9 3 8 2 6 0 1
from the same main class.

Crossrefs

Cf. A287761, A287762, A333671, A305571.

Sequence in context: A223419 A333671 A287762 * A305571 A229505 A299785

Adjacent sequences: A309596 A309597 A309598 * A309600 A309601 A309602

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Aug 09 2019

Status

approved