0,1

Also number of pure (= irreducible) group-testing histories of n items - A. Boneh, Mar 31, 2000

Also number of antichain covers of an unlabeled n-set, so a(n) equals first differences of A003182 - Vladeta Jovovic, Goran Kilibarda (vladeta(AT)Eunet.yu), Aug 18 2000

Also number of inequivalent (under permutation of variables) nondegenerate monotone Boolean functions of n variables. We say h and g (functions of n variables) are equivalent if there exists a permutation p of Sn such that hp=g. E.g. a(3)=5 because xyz, xy+xz+yz, x+yz+xyz, xy+xz+xyz, x+y+z+xy+xz+yz+xyz are 5 inequivalent nondegenerate monotone Boolean functions that generate (by permutation of variables) the other 4. For example, y+xz+xyz can be obtained from x+yz+xyz by permuting x with y. - Alan Veliz-Cuba (alanavc(AT)vt.edu), Jun 16 2006

Y. M. M. Bishop, S. E. Fienberg and P. W. Holland, Discrete Multivariate Analysis. MIT Press, 1975, p. 34.

V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)

V. Jovovic and G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

A. A. Mcintosh, personal communication.

a(n)=A007411(n)+1. Cf. A006126 (labeled case).

Sequence in context: A031148 A032238 A000619 this_sequence A049404 A083773 A096179

Adjacent sequences: A006599 A006600 A006601 this_sequence A006603 A006604 A006605

nonn,nice,hard

C. L. Mallows

a(6) from A. Boneh, 32 Hantkeh St., Haifa 34608, Israel, Mar 31, 2000.

Entry revised by njas, Jul 23 2006