A296061 Number of one-plane symmetric diagonal Latin squares of order 2n.

0, 96, 92160, 290830417920

Offset: 1

Author

Eduard I. Vatutin, Dec 04 2017

Keywords

• nonn
• more
• hard

Comments

One-plane symmetric diagonal Latin squares are vertically or horizontally symmetric diagonal Latin squares. a(n) is equal to 2*X-Y, where X is the number of horizontally symmetric diagonal Latin squares (sequence A292516), and Y is the number of doubly symmetric diagonal Latin squares (sequence A292517).

Examples

			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
A doubly symmetric diagonal Latin square:
  0 1 2 3 4 5 6 7
  3 2 7 6 1 0 5 4
  2 3 1 0 7 6 4 5
  6 7 5 4 3 2 0 1
  7 6 3 2 5 4 1 0
  4 5 0 1 6 7 2 3
  5 4 6 7 0 1 3 2
  1 0 4 5 2 3 7 6
		

Links

• E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, V. S. Titov, Investigation of the properties of symmetric diagonal Latin squares. Corrections. Intellectual and Information Systems (2017), pp. 30-36 (in Russian)
• Eduard I. Vatutin, Stepan E. Kochemazov, Oleq S. Zaikin, Maxim O. Manzuk, Natalia N. Nikitina, Vitaly S. Titov, Central symmetry properties for diagonal Latin squares, Problems of Information Technology (2019) No. 2, 3-8.
• 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

Crossrefs

Cf. A287649, A292516, A292517, A296060, A340546.

Formula

a(n) = 2*A292516(n) - A292517(n).