A336764 Maximum number of order 3 subsquares in a Latin square of order n.

0, 0, 1, 0, 0, 4, 7

Offset

1,6

Comments

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)

Links

Table of n, a(n) for n=1..7.

R. Bean, Critical sets in Latin squares and Associated Structures, Ph.D. Thesis, The University of Queensland, 2001.

K. Heinrich and W. Wallis, The Maximum Number of Intercalates in a Latin Square, Combinatorial Math. VIII, Proc. 8th Australian Conf. Combinatorics, 1980, 221-233.

I. M. Wanless, Latin Squares with One Subsquare, Journal of Combinatorial Designs, 9 (2001), 128-146.

Formula

a(3^n) = 9*a(3^(n-1)) + 27^(n-1) (conjectured).

Crossrefs

Cf. A092237, A091323, A090741, A307163, A307164.

Sequence in context: A146294 A133982 A069179 * A058377 A023961 A147863

Adjacent sequences: A336761 A336762 A336763 * A336765 A336766 A336767

Keyword

nonn,hard,more

Author

Omar Aceval Garcia, Cameron Byer, Eugene Fiorini, Nicholas Hanson, Brian G. Kronenthal, Lindsey Wise, Aug 03 2020

Status

approved