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A002860 Number of Latin squares of order n; or labeled quasigroups.
(Formerly M2051 N0812)
1, 2, 12, 576, 161280, 812851200, 61479419904000, 108776032459082956800, 5524751496156892842531225600, 9982437658213039871725064756920320000, 776966836171770144107444346734230682311065600000 (list; graph; refs; listen; history; text; internal format)



Berend, D. "On the number of Sudoku squares." Discrete Mathematics 341.11 (2018): 3241-3248. See p. 3241.

Clifford A. Pickover, The Math Book, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publ., NY, 2009.

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

H. J. Ryser, Combinatorial Mathematics. Mathematical Association of America, Carus Mathematical Monograph 14, 1963, p. 53.

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

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.

Ronald Alter, Research Problems: How Many Latin Squares are There?, Amer. Math. Monthly 82 (1975), no. 6, 632--634. MR1537769

S. E. Bammel and J. Rothstein, The number of 9x9 Latin squares, Discrete Math., 11 (1975), 93-95.

Jeranfer Bermúdez, Richard García, Reynaldo López and Lourdes Morales, Some Properties of Latin Squares, Laboratorio Emmy Noether, 2009.

J. W. Brown, Enumeration of Latin squares with application to order 8, J. Combin. Theory, 5 (1968), 177-184.

E. N. Gilbert, Latin squares which contain no repeated digrams, SIAM Rev. 7 1965 189--198. MR0179095 (31 #3346). Mentions this sequence. - N. J. A. Sloane, Mar 15 2014

A.-A. A. Jucys, The number of distinct Latin squares as a group-theoretical constant, J. Combinatorial Theory Ser. A 20 (1976), no. 3, 265--272. MR0419259 (54 #7283)

Dieter Jungnickel, Vladimir D. Tonchev, Counting Steiner triple systems with classical parameters and prescribed rank, arXiv:1709.06044 [math.CO], 2017.

B. D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.

B. D. McKay and I. M. Wanless, On the number of Latin squares. Preprint 2004.

B. D. McKay and I. M. Wanless, On the number of Latin squares, Ann. Combinat. 9 (2005) 335-344.

J. Shao and W. Wei, A formula for the number of Latin squares., Discrete Mathematics 110 (1992) 293-296.

Minjia Shi, Li Xu, Denis S. Krotov, The number of the non-full-rank Steiner triple systems, arXiv:1806.00009 [math.CO], 2018.

T. Sillke, How many Latin Squares of order-N are there?

D. S. Stones, The many formulas for the number of Latin rectangles, Electron. J. Combin 17 (2010), A1.

D. S. Stones and I. M. Wanless, Divisors of the number of Latin rectangles, J. Combin. Theory Ser. A 117 (2010), 204-215.

Eric Weisstein's World of Mathematics, Latin Square.

M. B. Wells, The number of Latin squares of order 8, J. Combin. Theory, 3 (1967), 98-99.

Krasimir Yordzhev, The bitwise operations in relation to obtaining Latin squares, arXiv preprint arXiv:1605.07171 [cs.OH], 2016.

Index entries for sequences related to Latin squares and rectangles

Index entries for sequences related to quasigroups


a(n) = n!*A000479(n) = n!*(n-1)!*A000315(n).


Cf. A000315, A000479.

Cf. A003090, A040082, A057991.

Cf. A098679 (Latin cubes).

A row of the array in A249026.

Sequence in context: A264952 A050643 A145513 * A108078 A052129 A216335

Adjacent sequences:  A002857 A002858 A002859 * A002861 A002862 A002863




N. J. A. Sloane.


One more term (from the McKay-Wanless article) from Richard Bean (rwb(AT)eskimo.com), Feb 17 2004



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Last modified December 11 22:04 EST 2018. Contains 318052 sequences. (Running on oeis4.)