A040082 Number of inequivalent Latin squares (or isotopy classes of Latin squares) of order n. (Formerly M0392 N0150)

1, 1, 1, 2, 2, 22, 564, 1676267, 115618721533, 208904371354363006, 12216177315369229261482540

Offset

1,4

Comments

Here "isotopy class" means an equivalence class of Latin squares under the operations of row permutation, column permutation and symbol permutation. - Brendan McKay

References

R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural and Medical Research. 6th ed., Hafner, NY, 1963, p. 22.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 210.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..11.

John Wesley Brown, Enumeration of Latin squares with application to order 8, J. Combin. Theory, 5 (1968), 177-184. [a(7) and a(8) appear to be given incorrectly. - N. J. A. Sloane, Jan 23 2020]

A. Hulpke, Petteri Kaski and Patric R. J. Östergård, The number of Latin squares of order 11, Math. Comp. 80 (2011) 1197-1219.

G. Kolesova, C. W. H. Lam and L. Thiel, On the number of 8 X 8 Latin squares, J. Combin. Theory, (A) 54 (1990) 143-148.

Brendan D. McKay, Latin Squares (has list of all such squares).

Brendan D. McKay, Alison Meynert and Wendy Myrvold, Small Latin Squares, Quasigroups and Loops, J. Combin. Designs 15 (2007), no. 2, 98-119.

Brendan D. McKay and Eric Rogoyski, Latin squares of order 10, Electron. J. Combinatorics, 2 (1995) #N3.

Eduard Vatutin, Alexey Belyshev, Stepan Kochemazov, Oleg Zaikin, and Natalia Nikitina, Enumeration of Isotopy Classes of Diagonal Latin Squares of Small Order Using Volunteer Computing, Russian Supercomputing Days (Суперкомпьютерные дни в России), 2018.

Eric Weisstein's World of Mathematics, Latin Square.

Mark B. Wells, The number of Latin squares of order eight, J. Combin. Theory, 3 (1967), 98-99.

Index entries for sequences related to Latin squares and rectangles

Crossrefs

Cf. A002860, A003090, A000315. See A000528 for another version.

Sequence in context: A385121 A357244 A001012 * A383154 A014358 A093355

Adjacent sequences: A040079 A040080 A040081 * A040083 A040084 A040085

Keyword

nonn,hard,nice

Author

N. J. A. Sloane

Extensions

7 X 7 and 8 X 8 results confirmed by Brendan McKay

Beware: erroneous versions of this sequence can be found in the literature!

a(9)-a(10) (from the McKay-Meynert-Myrvold article) from Richard Bean, Feb 17 2004

a(11) from Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009

Status

approved