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A023815
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Number of binary operations on an n-set that are commutative and associative; labeled commutative semigroups.
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12
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..9.
Eric Postpischil Posting to sci.math newsgroup, May 21 1990
Amit Sehgal, Sunil Kumar, Sarita, Yashpal, Commutative Associative Binary Operations on a Set with Five Elements, J. Phys.: Conf. Ser. (2018) 1000 012063
Eric Weisstein's World of Mathematics, Semigroup.
Index entries for sequences related to semigroups
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FORMULA
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a(n) + A079192(n) + A079195(n) + A079198(n) = A002489(n).
a(n) = Sum_{k>=1} A079201(n,k)*A079210(n,k). - Andrew Howroyd, Jan 26 2022
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CROSSREFS
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Row sums of A058167.
Cf. A001423, A001426 (isomorphism classes), A023813 (commutative only), A023814 (associative only), A027851.
Cf. A002489, A079192, A079195, A079198, A079201, A079210.
Sequence in context: A271607 A360481 A079244 * A249590 A034665 A218383
Adjacent sequences: A023812 A023813 A023814 * A023816 A023817 A023818
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KEYWORD
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nonn,hard,more
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AUTHOR
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Lyle Ramshaw (ramshaw(AT)pa.dec.com)
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EXTENSIONS
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a(8) from Andrew Howroyd, Jan 26 2022
a(9) from Andrew Howroyd, Feb 14 2022
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STATUS
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approved
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