

A326906


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


10




OFFSET

0,1


COMMENTS

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


LINKS

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


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.
Cf. A000798, A102896, A102897, A108800, A193675, A306445, A326880, A326881, A326883.
Sequence in context: A295382 A123642 A007848 * A303060 A270555 A270405
Adjacent sequences: A326903 A326904 A326905 * A326907 A326908 A326909


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Aug 03 2019


STATUS

approved



