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%I M2929 N1177 #43 Aug 06 2022 07:17:40
%S 1,1,3,12,58,325,2143,17291,221805,11545843,3518930337
%N Number of commutative semigroups of order n.
%D P. A. Grillet, Computing Finite Commutative Semigroups, Semigroup Forum 53 (1996), 140-154.
%D P. A. Grillet, Computing Finite Commutative Semigroups: Part II, Semigroup Forum 67 (2003), 159-184.
%D H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup Forum, 14 (1977), 69-79.
%D R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.
%D R. J. Plemmons, Cayley Tables for All Semigroups of Order Less Than 7. Department of Mathematics, Auburn Univ., 1965.
%D S. Satoh, K. Yama, and M. Tokizawa, Semigroups of order 8, Semigroup Forum 49 (1994), 7-29.
%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 Remigiusz Durka, Kamil Grela, <a href="https://arxiv.org/abs/1911.12814">On the number of possible resonant algebras</a>, arXiv:1911.12814 [hep-th], 2019.
%H H. Juergensen and P. Wick, <a href="/A001423/a001423.pdf">Die Halbgruppen von Ordnungen <= 7</a>, annotated and scanned copy.
%H R. J. Plemmons, <a href="/A001423/a001423_2.pdf">There are 15973 semigroups of order 6</a> (annotated and scanned copy)
%H Eric Postpischil <a href="http://groups.google.com/groups?&hl=en&lr=&ie=UTF-8&selm=11802%40shlump.nac.dec.com&rnum=2">Posting to sci.math newsgroup, May 21 1990</a> [Broken link]
%H N. J. A. Sloane, <a href="/A001329/a001329.jpg">Overview of A001329, A001423-A001428, A258719, A258720.</a>
%H T. Tamura, <a href="/A001329/a001329.pdf">Some contributions of computation to semigroups and groupoids</a>, pp. 229-261 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970. (Annotated and scanned copy)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semigroup.html">Semigroup.</a>
%H <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%Y Cf. A001423, A023815, A027851, A058105, A058116.
%Y a(n) + A079193(n) + A079196(n) + A079199(n) = A001329(n).
%K nonn,nice,hard,more
%O 0,3
%A _N. J. A. Sloane_
%E a(8) (from the Satoh et al. paper) supplied by Richard C. Schroeppel, Jul 22 2005
%E a(9) and a(10) from Grillet references sent by Jens Zumbragel (jzumbr(AT)math.unizh.ch), Jun 14 2006
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