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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)

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

AUTHOR

Eduard I. Vatutin, Oct 16 2017

STATUS

approved

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