A092237 Maximum number of intercalates in a Latin square of order n.

0, 1, 0, 12, 4, 27, 42, 112, 72

Offset

1,4

Comments

An intercalate is a 2 X 2 subsquare of a Latin square. a(10) >= 125, a(11) >= 172, a(12) >= 324.

References

I. Wanless, Private communication, 2003.

Links

Table of n, a(n) for n=1..9.

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.

Index entries for sequences related to Latin squares and rectangles

Formula

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.

Crossrefs

Cf. A091323, A090741.

Sequence in context: A199693 A166206 A040137 * A367323 A081987 A327972

Adjacent sequences: A092234 A092235 A092236 * A092238 A092239 A092240

Keyword

hard,nonn,more

Author

Richard Bean, Feb 17 2004

Status

approved