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A307839 Minimum number of Latin subrectangles in a diagonal Latin square of order n.

%I A307839 #29 Jun 13 2021 03:45:37
%S A307839 1,0,0,137,336,884,1968,4545
%N A307839 Minimum number of Latin subrectangles in a diagonal Latin square of order n.
%C A307839 An Latin subrectangle is a m X k Latin rectangle of a Latin square of order n, 1 <= m <= n, 1 <= k <= n.
%H A307839 E. I. Vatutin, <a href="http://forum.boinc.ru/default.aspx?g=posts&amp;m=92687#post92687">Discussion about properties of diagonal Latin squares at forum.boinc.ru</a> (in Russian).
%H A307839 E. I. Vatutin, <a href="https://vk.com/wall162891802_1323">About the minimum and maximum number of Latin subrectangles in a diagonal Latin squares of order 8</a> (in Russian).
%H A307839 Eduard Vatutin, Alexey Belyshev, Natalia Nikitina, and Maxim Manzuk, <a href="https://doi.org/10.1007/978-3-030-66895-2_9">Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10</a>, High-Performance Computing Systems and Technologies in Sci. Res., Automation of Control and Production (HPCST 2020), Communications in Comp. and Inf. Sci. book series (CCIS, Vol. 1304) Springer (2020), 127-146.
%H A307839 Eduard I. Vatutin, <a href="/A307839/a307839.txt">Proving list (best known examples)</a>.
%H A307839 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A307839 For example, the square
%e A307839   0 1 2 3 4 5 6
%e A307839   4 2 6 5 0 1 3
%e A307839   3 6 1 0 5 2 4
%e A307839   6 3 5 4 1 0 2
%e A307839   1 5 3 2 6 4 0
%e A307839   5 0 4 6 2 3 1
%e A307839   2 4 0 1 3 6 5
%e A307839 has a Latin subrectangle
%e A307839   . . . . . . .
%e A307839   . . 6 5 0 1 3
%e A307839   . . . . . . .
%e A307839   . . . . . . .
%e A307839   . . . . . . .
%e A307839   . . . . . . .
%e A307839   . . 0 1 3 6 5
%e A307839 The total number of Latin subrectangles for this square is 2119.
%Y A307839 Cf. A274806, A307163, A307164, A307840, A307841, A307842.
%K A307839 nonn,more,hard
%O A307839 1,4
%A A307839 _Eduard I. Vatutin_, May 01 2019
%E A307839 a(8) added by _Eduard I. Vatutin_, Oct 06 2020