cp's OEIS Frontend

A001426 Number of commutative semigroups of order n.

%I A001426 M2929 N1177 #46 Aug 15 2025 04:55:22
%S A001426 1,1,3,12,58,325,2143,17291,221805,11545843,3518930337
%N A001426 Number of commutative semigroups of order n.
%D A001426 P. A. Grillet, Computing Finite Commutative Semigroups, Semigroup Forum 53 (1996), 140-154.
%D A001426 P. A. Grillet, Computing Finite Commutative Semigroups: Part II, Semigroup Forum 67 (2003), 159-184.
%D A001426 R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.
%D A001426 R. J. Plemmons, Cayley Tables for All Semigroups of Order Less Than 7. Department of Mathematics, Auburn Univ., 1965.
%D A001426 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001426 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001426 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 A001426 H. Juergensen and P. Wick, <a href="https://gdz.sub.uni-goettingen.de/id/PPN362162808_0014">Die Halbgruppen von Ordnungen <= 7</a>, Semigroup Forum, 14 (1977), 69-79.
%H A001426 H. Juergensen and P. Wick, <a href="/A001423/a001423.pdf">Die Halbgruppen von Ordnungen <= 7</a>, annotated and scanned copy.
%H A001426 R. J. Plemmons, <a href="/A001423/a001423_2.pdf">There are 15973 semigroups of order 6</a> (annotated and scanned copy)
%H A001426 Eric Postpischil <a href="http://groups.google.com/groups?&amp;hl=en&amp;lr=&amp;ie=UTF-8&amp;selm=11802%40shlump.nac.dec.com&amp;rnum=2">Posting to sci.math newsgroup, May 21 1990</a> [Broken link]
%H A001426 S. Satoh, K. Yama, M. Tokizawa, <a href="https://gdz.sub.uni-goettingen.de/id/PPN362162808_0049">Semigroups of order 8</a>, Semigroup Forum 49 (1994), 7-29.
%H A001426 N. J. A. Sloane, <a href="/A001329/a001329.jpg">Overview of A001329, A001423-A001428, A258719, A258720.</a>
%H A001426 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 A001426 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semigroup.html">Semigroup.</a>
%H A001426 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%Y A001426 Cf. A001423, A023815, A027851, A058105, A058116.
%Y A001426 a(n) + A079193(n) + A079196(n) + A079199(n) = A001329(n).
%K A001426 nonn,nice,hard,more
%O A001426 0,3
%A A001426 _N. J. A. Sloane_
%E A001426 a(8) (from the Satoh et al. paper) supplied by Richard C. Schroeppel, Jul 22 2005
%E A001426 a(9) and a(10) from Grillet references sent by Jens Zumbragel (jzumbr(AT)math.unizh.ch), Jun 14 2006