%I M0392 N0150 #36 Feb 02 2020 21:35:12

%S 1,1,1,2,2,22,564,1676267,115618721533,208904371354363006,

%T 12216177315369229261482540

%N Number of inequivalent Latin squares (or isotopy classes of Latin squares) of order n.

%C Here "isotopy class" means an equivalence class of Latin squares under the operations of row permutation, column permutation and symbol permutation. [Brendan McKay]

%D R. A. Fisher and F. Yates, Statistical Tables for Biological, Agricultural and Medical Research. 6th ed., Hafner, NY, 1963, p. 22.

%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 210.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H J. W. Brown, <a href="http://dx.doi.org/10.1016/S0021-9800(68)80053-5">Enumeration of Latin squares with application to order 8</a>, J. Combin. Theory, 5 (1968), 177-184. [a(7) and a(8) appear to be given incorrectly. - _N. J. A. Sloane_, Jan 23 2020]

%H A. Hulpke, Petteri 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 G. Kolesova, C. W. H. Lam and L. Thiel, <a href="https://doi.org/10.1016/0097-3165(90)90015-O">On the number of 8x8 Latin squares</a>, J. Combin. Theory,(A) 54 (1990) 143-148.

%H 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 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 Brendan 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 Eduard Vatutin, Alexey Belyshev, Stepan Kochemazov, Oleg Zaikin, Natalia Nikitina, <a href="http://russianscdays.org/files/pdf18/933.pdf">Enumeration of Isotopy Classes of Diagonal Latin Squares of Small Order Using Volunteer Computing</a>, Russian Supercomputing Days (Суперкомпьютерные дни в России), 2018.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LatinSquare.html">Latin Square</a>

%H M. B. Wells, <a href="http://dx.doi.org/10.1016/0097-3165(90)90015-O">The number of Latin squares of order 8</a>, J. Combin. Theory, 3 (1967), 98-99.

%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>

%Y Cf. A002860, A003090, A000315. See A000528 for another version.

%K nonn,hard,nice

%O 1,4

%A _N. J. A. Sloane_

%E 7 X 7 and 8 X 8 results confirmed by _Brendan McKay_

%E Beware: erroneous versions of this sequence can be found in the literature!

%E a(9)-a(10) (from the McKay-Meynert-Myrvold article) from _Richard Bean_, Feb 17 2004

%E a(11) from Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009