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A292517 Number of doubly symmetric diagonal Latin squares of order 2n. 4
0, 48, 0, 495452160 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Doubly symmetric square has symmetries both in horizontal and vertical planes.

One plane symmetry requires one-to-one correspondens between values of elements a[i][j] and a[N-i][j] in vertical plane and between values of elements a[i][j] and a[i][N-j] in horizontal plane for all i and j values (numbering if indexes from 1). - Eduard I. Vatutin, Alexey D. Belyshev, Oct 09 2017

It seems that doubly symmetric diagonal Latin squares exists only for orders N == 0 (mod 4). - Eduard I. Vatutin, Oct 18 2017

LINKS

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

E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru, corrected value a(4) (in Russian)

E. I. Vatutin, S. E. Kochemazov, 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, 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, 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. 30-36 (in Russian)

Index entries for sequences related to Latin squares and rectangles

FORMULA

a(n) = A287650(n)*n!.

EXAMPLE

Doubly symmetric diagonal Latin square example:

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

In the horizontal direction there is a one-to-one correspondence between elements 0 and 7, 1 and 6, 2 and 5, 3 and 4.

In the vertical direction there is also a correspondence between elements 0 and 1, 2 and 4, 6 and 7, 3 and 5.

CROSSREFS

Cf. A003191, A287649, A287650.

Sequence in context: A002834 A057380 A234565 * A036210 A257875 A037941

Adjacent sequences:  A292514 A292515 A292516 * A292518 A292519 A292520

KEYWORD

nonn,more,bref

AUTHOR

Eduard I. Vatutin, Sep 18 2017

EXTENSIONS

a(4) corrected by Eduard I. Vatutin, Alexey D. Belyshev, Oct 09 2017

STATUS

approved

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Last modified July 17 01:41 EDT 2018. Contains 312693 sequences. (Running on oeis4.)