A340546 Number of main classes of diagonal Latin squares of order 2n that contain a one-plane symmetric square.

0, 1, 2, 9717

Offset

1,3

Comments

A one-plane symmetric diagonal Latin square is a vertically or horizontally symmetric diagonal Latin square (see A296060). Such diagonal Latin squares do not exist for odd orders > 1.

Links

Table of n, a(n) for n=1..4.

Eduard I. Vatutin, On the number of main classes of one plane and double plane symmetric diagonal Latin squares of orders 1-8 (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)

Index entries for sequences related to Latin squares and rectangles.

Example

A horizontally symmetric diagonal Latin square:
  0 1 2 3 4 5
  4 2 0 5 3 1
  5 4 3 2 1 0
  2 5 4 1 0 3
  3 0 1 4 5 2
  1 3 5 0 2 4
A vertically symmetric diagonal Latin square:
  0 1 2 3 4 5
  4 2 5 0 3 1
  3 5 1 2 0 4
  5 3 0 4 1 2
  2 4 3 1 5 0
  1 0 4 5 2 3
Both are one-plane symmetric diagonal Latin squares.

Crossrefs

Cf. A287649, A287764, A292516, A293777, A293778, A296060, A296061, A340550.

Sequence in context: A167748 A203755 A285692 * A343700 A086563 A023328

Adjacent sequences: A340543 A340544 A340545 * A340547 A340548 A340549

Keyword

nonn,more,hard,bref

Author

Eduard I. Vatutin, Jan 11 2021

Extensions

Name clarified by Andrew Howroyd, Oct 22 2023

Status

approved