

A307839


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


2




OFFSET

1,4


COMMENTS

An Latin subrectangle is a 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..8.
E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian).
E. I. Vatutin, About the minimum and maximum number of Latin subrectangles in a diagonal Latin squares of order 8 (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 Latin subrectangle
. . . . . . .
. . 6 5 0 1 3
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
. . 0 1 3 6 5
The total number of Latin subrectangles for this square is 2119.


CROSSREFS

Cf. A274806, A307163, A307164, A307840, A307841, A307842.
Sequence in context: A325085 A142497 A142523 * A307840 A142211 A142447
Adjacent sequences: A307836 A307837 A307838 * A307840 A307841 A307842


KEYWORD

nonn,more


AUTHOR

Eduard I. Vatutin, May 01 2019


EXTENSIONS

a(8) added by Eduard I. Vatutin, Oct 06 2020


STATUS

approved



