

A108798


Number of nonisomorphic systems enumerated by A102894; that is, the number of inequivalent closure operators in which the empty set is closed. Also, the number of unionclosed sets with n elements that contain the universe and the empty set.


15




OFFSET

0,3


COMMENTS

Also the number of unlabeled finite sets of subsets of {1..n} that contain {} and {1..n} and are closed under intersection.  Gus Wiseman, Aug 02 2019


LINKS

Table of n, a(n) for n=0..7.
Bonacina, Maria Paola; Dershowitz, Nachum
Canonical ground Horn theories, Lecture Notes in Computer Science 7797, 3571 (2013).
G. Brinkmann and R. Deklerck, Generation of UnionClosed Sets and Moore Families, Journal of Integer Sequences, Vol.21 (2018), Article 18.1.7.
G. Brinkmann and R. Deklerck, Generation of UnionClosed Sets and Moore Families, arXiv:1701.03751 [math.CO], 2017


FORMULA

a(n) = A108800(n)/2.


EXAMPLE

From Gus Wiseman, Aug 02 2019: (Start)
Nonisomorphic representatives of the a(0) = 1 through a(3) = 14 unionclosed sets of sets:
{} {}{1} {}{12} {}{123}
{}{2}{12} {}{3}{123}
{}{1}{2}{12} {}{23}{123}
{}{1}{23}{123}
{}{3}{23}{123}
{}{13}{23}{123}
{}{2}{3}{23}{123}
{}{2}{13}{23}{123}
{}{3}{13}{23}{123}
{}{12}{13}{23}{123}
{}{2}{3}{13}{23}{123}
{}{3}{12}{13}{23}{123}
{}{2}{3}{12}{13}{23}{123}
{}{1}{2}{3}{12}{13}{23}{123}
(End)


CROSSREFS

The labeled version is A102894.
Cf. A000612, A001930, A003180, A102895, A102897, A108800, A193674, A193675, A326867, A326869, A326883.
Sequence in context: A090897 A120459 A272368 * A260995 A220438 A250001
Adjacent sequences: A108795 A108796 A108797 * A108799 A108800 A108801


KEYWORD

nonn,more


AUTHOR

Don Knuth, Jul 01 2005


EXTENSIONS

a(6) added (using A193674) by N. J. A. Sloane, Aug 02 2011
Added a(7), and reference to unionclosed sets.  Gunnar Brinkmann, Feb 05 2018


STATUS

approved



