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%I #12 Jan 22 2024 06:04:38
%S 0,1,0,12,4,27,42,112,72
%N Maximum number of intercalates in a Latin square of order n.
%C An intercalate is a 2 X 2 subsquare of a Latin square. a(10) >= 125, a(11) >= 172, a(12) >= 324.
%D I. Wanless, Private communication, 2003.
%H R. Bean, <a href="https://www.researchgate.net/publication/2416446_Critical_Sets_in_Latin_Squares_and_Associated_Structures">Critical sets in Latin squares and associated structures</a>, Ph.D. Thesis, The University of Queensland, 2001.
%H K. Heinrich and W. Wallis, <a href="https://doi.org/10.1007/BFb0091822">The maximum number of intercalates in a Latin square</a>, Combinatorial Math. VIII, Proc. 8th Australian Conf. Combinatorics, 1980, 221-233.
%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>
%F If n is a power of 2, a(n) = n^2*(n-1)/4; if n is one less than a power of 2, a(n) = n*(n-1)*(n-3)/4.
%Y Cf. A091323, A090741.
%K hard,nonn,more
%O 1,4
%A _Richard Bean_, Feb 17 2004
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