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%I #13 Oct 05 2020 05:06:31
%S 0,0,1,0,0,4,7
%N Maximum number of order 3 subsquares in a Latin square of order n.
%C A subsquare of a Latin square is a submatrix (not necessarily consisting of adjacent entries) which is itself a Latin square. (I. M. Wanless, Latin Squares with One Subsquare, Wiley and Sons)
%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 I. M. Wanless, <a href="http://users.monash.edu.au/~iwanless/abstracts/uniqsbsq.html">Latin Squares with One Subsquare</a>, Journal of Combinatorial Designs, 9 (2001), 128-146.
%F a(3^n) = 9*a(3^(n-1)) + 27^(n-1) (conjectured).
%Y Cf. A092237, A091323, A090741, A307163, A307164.
%K nonn,hard,more
%O 1,6
%A _Omar Aceval Garcia_, _Cameron Byer_, _Eugene Fiorini_, _Nicholas Hanson_, _Brian G. Kronenthal_, _Lindsey Wise_, Aug 03 2020