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A307839
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Minimum number of Latin subrectangles in a diagonal Latin square of order n.
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2
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OFFSET
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1,4
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COMMENTS
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An Latin subrectangle is a m X k Latin rectangle of a Latin square of order n, 1 <= m <= n, 1 <= k <= n.
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LINKS
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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
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EXAMPLE
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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.
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CROSSREFS
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Cf. A274806, A307163, A307164, A307840, A307841, A307842.
Sequence in context: A325085 A142497 A142523 * A307840 A142211 A142447
Adjacent sequences: A307836 A307837 A307838 * A307840 A307841 A307842
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KEYWORD
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nonn,more
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AUTHOR
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Eduard I. Vatutin, May 01 2019
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EXTENSIONS
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a(8) added by Eduard I. Vatutin, Oct 06 2020
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STATUS
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approved
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