

A003090


Number of species (or "main classes" or "paratopy classes") of Latin squares of order n.
(Formerly M0387)


12



1, 1, 1, 2, 2, 12, 147, 283657, 19270853541, 34817397894749939, 2036029552582883134196099
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 231.
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.
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, Latin Squares (has list of all such squares)
B. D. McKay, A. Meynert and W. Myrvold, Small Latin Squares, Quasigroups and Loops, J. Combin. Designs, 15 (2007), no. 2, 98119.
B. D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.
M. G. Palomo, Latin polytopes, arXiv preprint arXiv:1402.0772 [math.CO], 20142016.
Giancarlo Urzua, On line arrangements with applications to 3nets. arXiv:0704.0469 [math.AG], 20072009 (see page 9).
Ian M. Wanless, A Generalization of Transversals for Latin Squares, Electronic Journal of Combinatorics, volume 9, number 1 (2002), R12.
M. B. Wells, Elements of Combinatorial Computing, Pergamon, Oxford, 1971. [Annotated scanned copy of pages 237240]
Index entries for sequences related to Latin squares and rectangles


CROSSREFS

Cf. A000315, A002860, A040082.
Sequence in context: A032320 A032227 A032069 * A032152 A032057 A130718
Adjacent sequences: A003087 A003088 A003089 * A003091 A003092 A003093


KEYWORD

nonn,nice,hard


AUTHOR

N. J. A. Sloane.


EXTENSIONS

a(9)a(10) (from the McKayMeynertMyrvold article) from Richard Bean (rwb(AT)eskimo.com), Feb 17 2004
a(11) from Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009


STATUS

approved



