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A000315 Number of reduced Latin squares of order n; labeled loops (quasigroups with an identity element) and a fixed identity.
(Formerly M3690 N1508)
+0
14
1, 1, 1, 4, 56, 9408, 16942080, 535281401856, 377597570964258816, 7580721483160132811489280, 5363937773277371298119673540771840 (list; graph; listen)
OFFSET

1,4

REFERENCES

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

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

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

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 183.

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

B. D. McKay and I. M. Wanless, Latin squares of order eleven. Preprint 2004. http://cs.anu.edu.au/~bdm/papers/ls11.pdf

C. R. Rao, S. K. Mitra and A. Matthai, editors, Formulae and Tables for Statistical Work. Statistical Publishing Society, Calcutta, India, 1966, p. 193.

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.

M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, p. 240.

B. D. McKay and I. M. Wanless, On the number of Latin squares. Preprint 2004. http://cs.anu.edu.au/~bdm/papers/ls11.pdf

LINKS

B. Cherowitzo, Comb. Structures Lecture Notes

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

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to Latin squares and rectangles

Index entries for sequences related to quasigroups

B. D. McKay, A. Meynert, W. Myrvold, Small latin squares, quasigroups and loops, J. Combin. Designs, vol. 15, no. 2 (2007) pp 98-119.

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

CROSSREFS

a(n) = A002860(n)/(n!*(n-1)!) = A000479(n)/(n-1)!. Cf. A003090, A040082, A057771, A057997.

Sequence in context: A000573 A070019 A056075 this_sequence A080984 A071579 A060497

Adjacent sequences: A000312 A000313 A000314 this_sequence A000316 A000317 A000318

KEYWORD

nonn,hard,nice,more

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

Added 6/95: the last (10th) term was probably first computed by Eric Rogoyski

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

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.


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