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A326906 Number of sets of subsets of {1..n} that are closed under union and cover all n vertices. 10
2, 2, 8, 90, 4542, 2747402, 151930948472, 28175295407840207894 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 19 13:25 EST 2020. Contains 332044 sequences. (Running on oeis4.)