

A000528


Number of types of Latin squares of order n. Equivalently, number of nonisomorphic 1factorizations of K_{n,n}.


2



1, 1, 1, 2, 2, 17, 324, 842227, 57810418543, 104452188344901572, 6108088657705958932053657
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


COMMENTS

Here "type" means an equivalence class of Latin squares under the operations of row permutation, column permutation, symbol permutation and transpose. In the 1factorizations formulation, these operations are labeling of left side, labeling of right side, permuting the order in which the factors are listed and swapping the left and right sides, respectively.  Brendan McKay
There are 6108088657705958932053657 isomorphism classes of onefactorizations of $K_{11,11}$.  Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009


REFERENCES

CRC Handbook of Combinatorial Designs, 1996, p. 660.
Denes and Keedwell, Latin Squares and Applications, Academic Press 1974.


LINKS

Table of n, a(n) for n=1..11.
A. Hulpke, P. Kaski and P. R. J. Ostergard, The number of Latin squares of order 11, Math. Comp. 80 (2011) 11971219
B. D. McKay, A. Meynert and W. Myrvold, Small Latin Squares, Quasigroups and Loops, J. Combin. Designs, to appear (2005).
Index entries for sequences related to Latin squares and rectangles


CROSSREFS

See A040082 for another version.
Cf. A002860, A003090, A000315, A040082, A000479.
Sequence in context: A238289 A206095 A222451 * A260478 A074970 A297794
Adjacent sequences: A000525 A000526 A000527 * A000529 A000530 A000531


KEYWORD

hard,nonn,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Richard Bean (rwb(AT)eskimo.com), Feb 17 2004


STATUS

approved



