# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a001423 Showing 1-1 of 1 %I A001423 M3550 N1438 #71 Mar 24 2021 11:32:59 %S A001423 1,1,4,18,126,1160,15973,836021,1843120128,52989400714478, %T A001423 12418001077381302684 %N A001423 Number of semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator). %D A001423 David Nacin, "Puzzles, Parity Maps, and Plenty of Solutions", Chapter 15, The Mathematics of Various Entertaining Subjects: Volume 3 (2019), Jennifer Beineke & Jason Rosenhouse, eds. Princeton University Press, Princeton and Oxford, p. 245. %D A001423 R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23. %D A001423 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A001423 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A001423 A. de Vries, Formal Languages: An Introduction %H A001423 Andreas Distler, Classification and Enumeration of Finite Semigroups, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010). %H A001423 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] %H A001423 A. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv:1301.6023 [math.CO], 2013. %H A001423 Andreas Distler, Chris Jefferson, Tom Kelsey, and Lars Kotthoff, The Semigroups of Order 10, in: M. Milano (Ed.), Principles and Practice of Constraint Programming, 18th International Conference, CP 2012, Québec City, QC, Canada, October 8-12, 2012, Proceedings (LNCS, volume 7514), pp. 883-899, Springer-Verlag Berlin Heidelberg 2012. %H A001423 Remigiusz Durka and Kamil Grela, On the number of possible resonant algebras, arXiv:1911.12814 [hep-th], 2019. %H A001423 G. E. Forsythe, SWAC computes 126 distinct semigroups of order 4, Proc. Amer. Math. Soc. 6, (1955). 443-447. %H A001423 H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup Forum, 14 (1977), 69-79. %H A001423 H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, annotated and scanned copy. %H A001423 Daniel J. Kleitman, Bruce L. Rothschild and Joel H. Spencer, The number of semigroups of order n, Proc. Amer. Math. Soc., 55 (1976), 227-232. %H A001423 R. J. Plemmons, There are 15973 semigroups of order 6 (annotated and scanned copy) %H A001423 Eric Postpischil Associativity Problem, Posting to sci.math newsgroup, May 21 1990. %H A001423 S. Satoh, K. Yama, and M. Tokizawa, Semigroups of order 8, Semigroup Forum 49 (1994), 7-29. %H A001423 N. J. A. Sloane, Overview of A001329, A001423-A001428, A258719, A258720. %H A001423 T. Tamura, Some contributions of computation to semigroups and groupoids, pp. 229-261 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970. (Annotated and scanned copy) %H A001423 Eric Weisstein's World of Mathematics, Semigroup. %H A001423 Index entries for sequences related to semigroups %F A001423 a(n) = (A027851(n) + A029851(n))/2. %Y A001423 Cf. A001426, A023814, A058107, A058123, A151823. %K A001423 nonn,hard,more,nice %O A001423 0,3 %A A001423 _N. J. A. Sloane_ %E A001423 a(9) added by _Andreas Distler_, Jan 12 2011 %E A001423 a(10) from Distler et al. 2012, added by _Andrey Zabolotskiy_, Nov 08 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE