A326906 - OEIS

A326906

Number of sets of subsets of {1..n} that are closed under union and cover all n vertices.

2, 2, 8, 90, 4542, 2747402, 151930948472, 28175295407840207894

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OFFSET

0,1

COMMENTS

Differs from A102895 in having a(0) = 2 instead of 1.

LINKS

FORMULA

a(n) = 2 * A102894(n).

EXAMPLE

The a(0) = 2 through a(2) = 8 sets of subsets:

{} {{1}} {{1,2}}

{{}} {{},{1}} {{},{1,2}}

{{1},{1,2}}

{{2},{1,2}}

{{},{1},{1,2}}

{{},{2},{1,2}}

{{1},{2},{1,2}}

{{},{1},{2},{1,2}}

MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n]]], Union@@#==Range[n]&&SubsetQ[#, Union@@@Tuples[#, 2]]&]], {n, 0, 3}]

CROSSREFS

The case without empty sets is A102894.

The case with a single covering edge is A102895.

Binomial transform is A102897.

The case also closed under intersection is A326878 for n > 0.

The same for intersection instead of union is (also) A326906.

The unlabeled version is A326907.

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 03 2019

STATUS

approved