0,2

Or, number of Moore families on an n-set, that is, families of subsets that contain the universal set {1,...,n} and are closed under intersection.

Or, number of closure operators on a set of n elements.

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

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

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.

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

N. Dershowitz, G. S. Huang and M. Harris, Draft.

a(n) = sum( C(n, k)*A102894, k=0..n), where C(n, k) is the binomial coefficient

For asymptotics see A102897.

Cf. A102894, A102895, A102897, A108798, A108799, A108800, A108801.

Sequence in context: A046846 A111010 A089307 this_sequence A088107 A132524 A153694

Adjacent sequences: A102893 A102894 A102895 this_sequence A102897 A102898 A102899

nonn,hard,more

Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu), Jan 18 2005

N. J. A. Sloane (njas(AT)research.att.com) added a(6) from the Habib et al. reference, May 26 2005

Additional comments from D. E. Knuth, Jul 01, 2005