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A092237 Maximum number of intercalates in a Latin square of order n. 3
0, 1, 0, 12, 4, 27, 42, 112, 72 (list; graph; refs; listen; history; text; internal format)
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

a(2^n) = n^2(n-1)/4; a(2^n-1) = n(n-1)(n-3)/4

CROSSREFS

Cf. A091323, A090741.

Sequence in context: A199693 A166206 A040137 * A081987 A327972 A047709

Adjacent sequences:  A092234 A092235 A092236 * A092238 A092239 A092240

KEYWORD

hard,nonn

AUTHOR

Richard Bean, Feb 17 2004

STATUS

approved

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)