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A003090 Number of species (or "main classes" or "paratopy classes") of Latin squares of order n.
(Formerly M0387)
1, 1, 1, 2, 2, 12, 147, 283657, 19270853541, 34817397894749939, 2036029552582883134196099 (list; graph; refs; listen; history; text; internal format)



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).


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

Yue Guan, Minjia Shi, Denis S. Krotov, The Steiner triple systems of order 21 with a transversal subdesign TD(3,6), arXiv:1905.09081 [math.CO], 2019.

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

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

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

Brendan 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], 2014-2016.

Giancarlo Urzua, On line arrangements with applications to 3-nets, arXiv:0704.0469 [math.AG], 2007-2009 (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 237-240]

Index entries for sequences related to Latin squares and rectangles


Cf. A000315, A002860, A040082.

Sequence in context: A032320 A032227 A032069 * A032152 A032057 A130718

Adjacent sequences:  A003087 A003088 A003089 * A003091 A003092 A003093




N. J. A. Sloane


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



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Last modified July 11 10:09 EDT 2020. Contains 335626 sequences. (Running on oeis4.)