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A001423 Number of semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
(Formerly M3550 N1438)
+0
14
1, 1, 4, 18, 126, 1160, 15973, 836021, 1843120128 (list; graph; listen)
OFFSET

0,3

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).

Andreas Distler and Tom Kelsey, The Monoids of Order Eight and Nine, in Intelligent Computer Mathematics, Lecture Notes in Computer Science, Volume 5144/2008, Springer-Verlag. [From N. J. A. Sloane, Jul 10 2009]

G. E. Forsythe, SWAC computes 126 distinct semigroups of order 4, Proc. Amer. Math. Soc. 6, (1955). 443-447.

H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup Forum, 14 (1977), 69-79.

D. J. Kleitman, B. L. Rothschild and J. H. Spencer, The number of semigroups of order n, Proc. Amer. Math. Soc., 55 (1976), 227-232.

R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.

Satoh, S.; Yama, K.; and Tokizawa, M., Semigroups of order 8, Semigroup Forum 49 (1994), 7-29.

LINKS

Eric Postpischil Posting to sci.math newsgroup, May 21 1990

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

Index entries for sequences related to semigroups

CROSSREFS

a(n)=(A027851(n)+A029851(n))/2. Cf. A001426, A023814, A058107, A058123, A151823.

Adjacent sequences: A001420 A001421 A001422 this_sequence A001424 A001425 A001426

Sequence in context: A112294 A073511 A108704 this_sequence A158341 A144272 A034517

KEYWORD

nonn,hard,nice

AUTHOR

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

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Last modified November 8 07:45 EST 2009. Contains 166143 sequences.


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