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A342998

Minimum number of diagonal transversals in a cyclic diagonal Latin square of order 2n+1.

1, 0, 5, 27, 0, 4523, 128818, 0, 204330233, 11232045257 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	COMMENTS	`A cyclic Latin square is a Latin square in which row i is obtained by cyclically shifting row i-1 by d places (see A338562, A123565 and A341585).` `Cyclic diagonal Latin squares do not exist for even orders.` `a(n) <= A342997(n).` `All cyclic diagonal Latin squares are diagonal Latin squares, so A287647(n) <= a((n-1)/2).`
	LINKS	`Table of n, a(n) for n=0..9.` `Eduard I. Vatutin, Enumerating the diagonal transversals for cyclic diagonal Latin squares of orders 1-19 (in Russian).` `Eduard I. Vatutin, Proving list (best known examples).` `Index entries for sequences related to Latin squares and rectangles.`
	EXAMPLE	`For n=2 one of best cyclic diagonal Latin squares of order 5` `0 1 2 3 4` `2 3 4 0 1` `4 0 1 2 3` `1 2 3 4 0` `3 4 0 1 2` `has a(2)=5 diagonal transversals:` `0 . . . . . 1 . . . . . 2 . . . . . 3 . . . . . 4` `. . 4 . . . . . 0 . . . . . 1 2 . . . . . 3 . . .` `. . . . 3 4 . . . . . 0 . . . . . 1 . . . . . 2 .` `. 2 . . . . . 3 . . . . . 4 . . . . . 0 1 . . . .` `. . . 1 . . . . . 2 3 . . . . . 4 . . . . . 0 . .`
	CROSSREFS	`Cf. A006717, A123565, A287647, A287648, A338562, A341585, A342997.` `Sequence in context: A081089 A180928 A366332 * A342997 A118391 A196085` `Adjacent sequences: A342995 A342996 A342997 * A342999 A343000 A343001`
	KEYWORD	`nonn,more,hard`
	AUTHOR	`Eduard I. Vatutin, Apr 02 2021`
	STATUS	`approved`

Last modified September 11 14:42 EDT 2024. Contains 375836 sequences. (Running on oeis4.)