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A307842 Maximum number of nontrivial Latin subrectangles in a diagonal Latin square of order n. 1
0, 0, 0, 12, 12, 51, 151 (list; graph; refs; listen; history; text; internal format)
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 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. A307840, A307841.

Sequence in context: A303646 A298036 A119877 * A147833 A003877 A161196

Adjacent sequences:  A307839 A307840 A307841 * A307844 A307845 A307846

KEYWORD

nonn,more

AUTHOR

Eduard I. Vatutin, May 01 2019

STATUS

approved

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Last modified July 19 12:35 EDT 2019. Contains 325159 sequences. (Running on oeis4.)