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A293778 Number of centrally symmetric diagonal Latin squares of order n. 1
1, 0, 0, 48, 960, 0, 14192640, 5449973760, 118753937326080 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Centrally symmetric diagon Latin square is a square with one-to-one correspondence between elements within all pairs a[i][j] and a[n-1-i][n-1-j] (numbering of rows and columns from 0 to n-1).

It seems that a(n)=0 for n=2 and n=3 (diagonal Latin squares of these sizes don't exist) and for n=2 (mod 4).

LINKS

Table of n, a(n) for n=1..9.

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, M. O. Manzuk, N. N. Nikitina, V. S. Titov, Properties of central symmetry for diagonal Latin squares, High-performance computing systems and technologies, No. 1 (8), 2018, pp. 74-78. (in Russian)

E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, M. O. Manzuk, N. N. Nikitina, V. S. Titov, Central Symmetry Properties for Diagonal Latin Squares, Problems of Information Technology, No. 2, 2019, pp. 3-8. doi: 10.25045/jpit.v10.i2.01.

Index entries for sequences related to Latin squares and rectangles

FORMULA

a(n) = A293777(n) * n!.

EXAMPLE

0 1 2 3 4 5 6 7 8

6 3 0 2 7 8 1 4 5

3 2 1 8 6 7 0 5 4

7 8 6 5 1 3 4 0 2

8 6 4 7 2 0 5 3 1

2 7 5 6 8 4 3 1 0

5 4 7 0 3 1 8 2 6

4 5 8 1 0 2 7 6 3

1 0 3 4 5 6 2 8 7

CROSSREFS

Cf. A292516, A292517, A293777.

Sequence in context: A233177 A014703 A233674 * A089903 A274806 A292045

Adjacent sequences:  A293775 A293776 A293777 * A293779 A293780 A293781

KEYWORD

nonn,more,changed

AUTHOR

Eduard I. Vatutin, Oct 16 2017

STATUS

approved

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Last modified October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)