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A326883 Number of unlabeled set-systems with {} that are closed under intersection and cover n vertices. 9
1, 1, 4, 22, 302, 28630, 216533404, 5592325966377736 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..7.

FORMULA

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

EXAMPLE

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.

Sequence in context: A195227 A265908 A119009 * A317803 A053722 A336212

Adjacent sequences:  A326880 A326881 A326882 * A326884 A326885 A326886

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 30 2019

EXTENSIONS

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

STATUS

approved

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Last modified September 27 22:36 EDT 2020. Contains 337388 sequences. (Running on oeis4.)