

A292516


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


3




OFFSET

1,2


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*XY, where Y is a number of double symmetric diagonal Latin squares (sequence A292517).  Eduard I. Vatutin, Alexey D. Belyshev, Oct 09 2017


LINKS

Table of n, a(n) for n=1..5.
E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, On Some Features of Symmetric Diagonal Latin Squares, CEUR WS, vol. 1940 (2017), pp. 7479.
E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, V. S. Titov, Investigation of the properties of symmetric diagonal Latin squares, Proceedings of the 10th multiconference on control problems (2017), vol. 3, pp. 1719 (in Russian)
E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian)
E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, V. S. Titov, Investigation of the properties of symmetric diagonal Latin squares. Working on errors, Intellectual and Information Systems (2017), pp. 3036 (in Russian)
Index entries for sequences related to Latin squares and rectangles


FORMULA

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


EXAMPLE

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


CROSSREFS

Cf. A003191, A287650, A287649.
Sequence in context: A164278 A159441 A011787 * A006070 A081262 A238001
Adjacent sequences: A292513 A292514 A292515 * A292517 A292518 A292519


KEYWORD

nonn,more


AUTHOR

Eduard I. Vatutin, Sep 18 2017


STATUS

approved



