A326907 Number of non-isomorphic sets of subsets of {1..n} that are closed under union and cover all n vertices. First differences of A193675.

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

Offset

0,1

Comments

Differs from A108800 in having a(0) = 2 instead of 1.

Links

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

Example

Non-isomorphic representatives of the a(0) = 2 through a(3) = 28 sets of sets:
  {}    {{1}}    {{12}}          {{123}}
  {{}}  {{}{1}}  {{}{12}}        {{}{123}}
                 {{2}{12}}       {{3}{123}}
                 {{}{2}{12}}     {{23}{123}}
                 {{1}{2}{12}}    {{}{3}{123}}
                 {{}{1}{2}{12}}  {{}{23}{123}}
                                 {{1}{23}{123}}
                                 {{3}{23}{123}}
                                 {{13}{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}{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}{13}{23}{123}}
                                 {{}{3}{12}{13}{23}{123}}
                                 {{2}{3}{12}{13}{23}{123}}
                                 {{}{2}{3}{12}{13}{23}{123}}
                                 {{1}{2}{3}{12}{13}{23}{123}}
                                 {{}{1}{2}{3}{12}{13}{23}{123}}

Crossrefs

The case without empty sets is A108798.

The case with a single covering edge is A108800.

First differences of A193675.

The case also closed under intersection is A326898 for n > 0.

The labeled version is A326906.

The same for union instead of intersection is (also) A326907.

Cf. A001930, A102895, A108798, A193674, A193675, A326880, A326881, A326883, A326898, A326908.

Sequence in context: A214446 A179320 A004304 * A270487 A058250 A179929

Adjacent sequences: A326904 A326905 A326906 * A326908 A326909 A326910

Keyword

nonn,more

Author

Gus Wiseman, Aug 03 2019

Extensions

a(7) added from A108800 by Andrew Howroyd, Aug 10 2019

Status

approved