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A102894 Number of ACI algebras or semilattices on n generators, with no identity or annihilator. 8
1, 1, 4, 45, 2271, 1373701, 75965474236, 14087647703920103947 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Or, number of families of subsets of {1, ..., n} that are closed under intersection and contain both the universe and the empty set.

An ACI algebra or semilattice is a system with a single binary, idempotent, commutative and associative operation.

REFERENCES

G. Birkhoff, Lattice Theory. American Mathematical Society, Colloquium Publications, Vol. 25, 3rd ed., Providence, RI, 1967.

Maria Paola Bonacina and Nachum Dershowitz, Canonical Inference for Implicational Systems, in Automated Reasoning, Lecture Notes in Computer Science, Volume 5195/2008, Springer-Verlag.

P. Colomb, A. Irlande and O. Raynaud, Counting of Moore Families for n=7, International Conference on Formal Concept Analysis (2010)

M. Habib and L. Nourine, The number of Moore families on n = 6, Discrete Math., 294 (2005), 291-296.

E. H. Moore, Introduction to a Form of General Analysis, AMS Colloquium Publication 2 (1910), pp. 53-80.

LINKS

Table of n, a(n) for n=0..7.

N. Dershowitz, G. S. Huang and M. Harris, Enumeration Problems Related to Ground Horn Theories, arXiv:cs/0610054v2 [cs.LO].

FORMULA

Inverse binomial transform of A102896.

For asymptotics see A102897.

CROSSREFS

Cf. A102895, A102896, A102897, A108798, A193674, A108800, A193675.

Sequence in context: A082765 A132873 A244753 * A132552 A189273 A288554

Adjacent sequences:  A102891 A102892 A102893 * A102895 A102896 A102897

KEYWORD

nonn,hard,more

AUTHOR

Mitch Harris, Jan 18 2005

EXTENSIONS

Additional comments from Don Knuth, Jul 01 2005

STATUS

approved

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Last modified November 14 03:52 EST 2018. Contains 317159 sequences. (Running on oeis4.)