A326883 Number of unlabeled set-systems with {} that are closed under intersection and cover n vertices.

1, 1, 4, 22, 302, 28630, 216533404, 5592325966377736

Offset: 0

Author

Gus Wiseman, Jul 30 2019

Keywords

• nonn
• more

Examples

			Non-isomorphic representatives of the a(0) = 1 through a(3) = 22 set-systems:
  {{}}  {{}{1}}  {{}{12}}        {{}{123}}
                 {{}{1}{2}}      {{}{1}{23}}
                 {{}{2}{12}}     {{}{3}{123}}
                 {{}{1}{2}{12}}  {{}{1}{2}{3}}
                                 {{}{23}{123}}
                                 {{}{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}}
		

Crossrefs

The case also closed under union is A001930.

The connected case (i.e., with maximum) is A108798.

The same for union instead of intersection is (also) A108798.

The non-covering case is A108800.

The labeled case is A326881.

Cf. A000798, A102894, A102895, A102897, A193674, A193675, A306445, A326875, A326878, A326880.

Formula

a(n) = A108800(n) - A108800(n-1) for n > 0. - Andrew Howroyd, Aug 10 2019

Extensions

a(5)-a(7) from Andrew Howroyd, Aug 10 2019