A293777 - OEIS

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A293777

Number of centrally symmetric diagonal Latin squares of order n with constant first row.

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)` `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`
	AUTHOR	`Eduard I. Vatutin, Oct 16 2017`
	STATUS	`approved`

Last modified January 18 05:30 EST 2019. Contains 319269 sequences. (Running on oeis4.)