A292516 Number of horizontally symmetric diagonal Latin squares of order 2n.

0, 48, 46080, 145662935040, 300216848351861145600

Offset: 1

Author

Eduard I. Vatutin, Sep 18 2017

Keywords

• nonn
• more
• hard

Comments

The number of horizontally symmetric diagonal Latin squares (X) is equal to the number of vertically symmetric diagonal Latin squares. The total number of symmetric diagonal Latin squares is equal to 2*X-Y, where Y is a number of double symmetric diagonal Latin squares (sequence A292517). - Eduard I. Vatutin, Alexey D. Belyshev, Oct 09 2017

Examples

			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
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
		

Links

• E. I. Vatutin, S. E. Kochemazov, and O. S. Zaikin, On Some Features of Symmetric Diagonal Latin Squares, CEUR WS, vol. 1940 (2017), pp. 74-79.
• E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, and V. S. Titov, Investigation of the properties of symmetric diagonal Latin squares, Proceedings of the 10th multiconference on control problems (2017), vol. 3, pp. 17-19 (in Russian)
• E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian)
• Eduard I. Vatutin, Stepan E. Kochemazov, Oleq S. Zaikin, Maxim O. Manzuk, Natalia N. Nikitina, and Vitaly S. Titov, Central symmetry properties for diagonal Latin squares, Problems of Information Technology (2019) No. 2, 3-8.
• E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, and V. S. Titov, Investigation of the properties of symmetric diagonal Latin squares. Working on errors, Intellectual and Information Systems (2017), pp. 30-36 (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.

Crossrefs

Cf. A003191, A287650, A287649, A296060, A296061, A340546.

Formula

a(n) = A287649(n) * (2*n)!.