cp's OEIS Frontend

A003090 Number of species (or "main classes" or "paratopy classes") of Latin squares of order n.

%I A003090 M0387 #55 Feb 02 2020 19:55:51
%S A003090 1,1,1,2,2,12,147,283657,19270853541,34817397894749939,
%T A003090 2036029552582883134196099
%N A003090 Number of species (or "main classes" or "paratopy classes") of Latin squares of order n.
%D A003090 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 231.
%D A003090 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003090 Yue Guan, Minjia Shi, Denis S. Krotov, <a href="https://arxiv.org/abs/1905.09081">The Steiner triple systems of order 21 with a transversal subdesign TD(3,6)</a>, arXiv:1905.09081 [math.CO], 2019.
%H A003090 A. Hulpke, P. Kaski and Patric R. J. Östergård, <a href="http://dx.doi.org/10.1090/S0025-5718-2010-02420-2">The number of Latin squares of order 11</a>, Math. Comp. 80 (2011) 1197-1219
%H A003090 Brendan D. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/data/latin.html">Latin Squares</a> (has list of all such squares)
%H A003090 Brendan D. McKay, A. Meynert and W. Myrvold, <a href="http://users.cecs.anu.edu.au/~bdm/papers/ls_final.pdf">Small Latin Squares, Quasigroups and Loops</a>, J. Combin. Designs, 15 (2007), no. 2, 98-119.
%H A003090 Brendan D. McKay and E. Rogoyski, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v2i1n3">Latin squares of order ten</a>, Electron. J. Combinatorics, 2 (1995) #N3.
%H A003090 M. G. Palomo, <a href="http://arxiv.org/abs/1402.0772">Latin polytopes</a>, arXiv preprint arXiv:1402.0772 [math.CO], 2014-2016.
%H A003090 Giancarlo Urzua, <a href="http://arXiv.org/abs/0704.0469">On line arrangements with applications to 3-nets</a>, arXiv:0704.0469 [math.AG], 2007-2009 (see page 9).
%H A003090 Ian M. Wanless, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v9i1r12">A Generalization of Transversals for Latin Squares</a>, Electronic Journal of Combinatorics, volume 9, number 1 (2002), R12.
%H A003090 M. B. Wells, <a href="/A000170/a000170.pdf">Elements of Combinatorial Computing</a>, Pergamon, Oxford, 1971. [Annotated scanned copy of pages 237-240]
%H A003090 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>
%Y A003090 Cf. A000315, A002860, A040082.
%K A003090 nonn,nice,hard
%O A003090 1,4
%A A003090 _N. J. A. Sloane_
%E A003090 a(9)-a(10) (from the McKay-Meynert-Myrvold article) from _Richard Bean_, Feb 17 2004
%E A003090 a(11) from  Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009