

A307841


Minimum number of nontrivial Latin subrectangles in a diagonal Latin square of order n.


1




OFFSET

1,4


COMMENTS

A Latin subrectangle is an m X k Latin rectangle of a Latin square of order n, 1 <= m <= n, 1 <= k <= n.
A nontrivial Latin subrectangle is an m X k Latin rectangle of a Latin square of order n, 1 < m < n, 1 < k < n.


LINKS

Table of n, a(n) for n=1..7.
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


EXAMPLE

For example, the square
0 1 2 3 4 5 6
4 2 6 5 0 1 3
3 6 1 0 5 2 4
6 3 5 4 1 0 2
1 5 3 2 6 4 0
5 0 4 6 2 3 1
2 4 0 1 3 6 5
has a nontrivial Latin subrectangle
. . . . . . .
. . 6 5 0 1 3
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . 0 1 3 6 5
The total number of Latin subrectangles for this square is 2119 and the number of nontrivial Latin subrectangles is only 151.


CROSSREFS

Cf. A307839, A307842.
Sequence in context: A307170 A225951 A278711 * A257949 A077351 A119530
Adjacent sequences: A307838 A307839 A307840 * A307842 A307844 A307845


KEYWORD

nonn,more


AUTHOR

Eduard I. Vatutin, May 01 2019


STATUS

approved



