

A108800


Number of nonisomorphic systems enumerated by A102895.


15




OFFSET

0,2


COMMENTS

Also the number of nonisomorphic sets of sets with {} that are closed under intersection. Also the number of nonisomorphic setsystems (without {}) covering n + 1 vertices and closed under intersection.  Gus Wiseman, Aug 05 2019


LINKS

Table of n, a(n) for n=0..7.
M. Habib and L. Nourine, The number of Moore families on n = 6, Discrete Math., 294 (2005), 291296.


FORMULA

a(n > 0) = 2 * A108798(n).


EXAMPLE

From Gus Wiseman, Aug 02 2019: (Start)
Nonisomorphic representatives of the a(0) = 1 through a(3) = 28 sets of sets with {} that are closed under intersection:
{} {} {} {}
{}{1} {}{1} {}{1}
{}{12} {}{12}
{}{1}{2} {}{123}
{}{2}{12} {}{1}{2}
{}{1}{2}{12} {}{1}{23}
{}{2}{12}
{}{3}{123}
{}{1}{2}{3}
{}{23}{123}
{}{1}{2}{12}
{}{1}{3}{23}
{}{2}{3}{123}
{}{3}{13}{23}
{}{1}{23}{123}
{}{3}{23}{123}
{}{1}{2}{3}{23}
{}{1}{2}{3}{123}
{}{2}{3}{13}{23}
{}{1}{3}{23}{123}
{}{2}{3}{23}{123}
{}{3}{13}{23}{123}
{}{1}{2}{3}{13}{23}
{}{1}{2}{3}{23}{123}
{}{2}{3}{13}{23}{123}
{}{1}{2}{3}{12}{13}{23}
{}{1}{2}{3}{13}{23}{123}
{}{1}{2}{3}{12}{13}{23}{123}
(End)


CROSSREFS

Except a(0) = 1, first differences of A193675.
The connected case (i.e., with maximum) is A108798.
The same for union instead of intersection is (also) A108798.
The labeled version is A102895.
The case also closed under union is A326898.
The covering case is A326883.
Cf. A001930, A102894, A102896, A102897, A193674, A326880, A326881.
Sequence in context: A002047 A126340 A277480 * A325507 A306793 A326359
Adjacent sequences: A108797 A108798 A108799 * A108801 A108802 A108803


KEYWORD

nonn,more


AUTHOR

Don Knuth, Jul 01 2005


EXTENSIONS

a(6) added (using A193675) by N. J. A. Sloane, Aug 02 2011
Changed a(0) from 2 to 1 by Gus Wiseman, Aug 02 2019
a(7) added (using A108798) by Andrew Howroyd, Aug 10 2019


STATUS

approved



