Search: id:A040082
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%I A040082 M0392 N0150
%S A040082 1,1,1,2,2,22,564,1676267,115618721533,208904371354363006,12216177315369229261482540
%N A040082 Number of inequivalent Latin squares (or isotopy classes of Latin squares) 
               of order n.
%C A040082 Here "isotopy class" means an equivalence class of Latin squares under 
               the operations of row permutation, column permutation and symbol 
               permutation. [Brendan McKay]
%D A040082 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A040082 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A040082 J. W. Brown, Enumeration of Latin squares with application to order 8, 
               J. Combin. Theory, 5 (1968), 177-184.
%D A040082 R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural 
               and Medical Research. 6th ed., Hafner, NY, 1963, p. 22.
%D A040082 G. Kolesova, C. W. H. Lam and L. Thiel, On the number of 8x8 Latin squares, 
               J. Combin. Theory,(A) 54 (1990) 143-148.
%D A040082 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               210.
%D A040082 M. B. Wells, The number of Latin squares of order 8, J. Combin. Theory, 
               3 (1967), 98-99.
%D A040082 A. Hulpke, P. Kaski and P. R. J. Ostergard, The number of Latin squares 
               of order 11, Preprint, 2009.
%H A040082 B. D. McKay, <a href="http://cs.anu.edu.au/~bdm/data/latin.html">Latin 
               Squares</a> (has list of all such squares)
%H A040082 B. D. McKay and E. Rogoyski, <a href="http://www.combinatorics.org/Volume_2/
               volume2.html#N3">Latin squares of order ten</a>, Electron. J. Combinatorics, 
               2 (1995) #N3.
%H A040082 <a href="Sindx_La.html#Latin">Index entries for sequences related to 
               Latin squares and rectangles</a>
%H A040082 B. D. McKay, A. Meynert and W. Myrvold, <a href="http://cs.anu.edu.au/
               ~bdm/papers/ls_final.pdf">Small Latin Squares, Quasigroups and Loops</
               a>, J. Combin. Designs, to appear (2005).
%H A040082 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LatinSquare.html">Latin Square</a>
%Y A040082 Cf. A002860, A003090, A000315. See A000528 for another version.
%Y A040082 Sequence in context: A118326 A087405 A001012 this_sequence A014358 A093355 
               A122962
%Y A040082 Adjacent sequences: A040079 A040080 A040081 this_sequence A040083 A040084 
               A040085
%K A040082 nonn,hard,nice
%O A040082 1,4
%A A040082 N. J. A. Sloane (njas(AT)research.att.com).
%E A040082 7 X 7 and 8 X 8 results confirmed by Brendan McKay (bdm(AT)cs.anu.edu.au)
%E A040082 Beware: erroneous versions of this sequence can be found in the literature!
%E A040082 Two more terms (from the McKay-Meynert-Myrvold article) from Richard 
               Bean (rwb(AT)eskimo.com), Feb 17 2004
%E A040082 There are 12216177315369229261482540 isotopy classes of Latin squares 
               of order 11. - Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 
               18 2009

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