A108800 Number of nonisomorphic systems enumerated by A102895.

1, 2, 6, 28, 330, 28960, 216562364, 5592326182940100

Offset: 0

Author

Don Knuth, Jul 01 2005

Keywords

• nonn
• more

Comments

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

Examples

			From _Gus Wiseman_, Aug 02 2019: (Start)
Non-isomorphic 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)
		

Links

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

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.

Formula

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

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