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A293777 Number of centrally symmetric diagonal Latin squares of order n with constant first row. 1
1, 0, 0, 2, 8, 0, 2816, 135168, 327254016 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Centrally symmetric diagonal 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) = A293778(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. A287649, A287650, A293778.

Sequence in context: A160636 A282626 A206712 * A200704 A257955 A024544

Adjacent sequences:  A293774 A293775 A293776 * A293778 A293779 A293780

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.)