A326909 Number of sets of subsets of {1..n} closed under union and intersection and covering all of the vertices.

2, 2, 7, 45, 500, 9053, 257151, 11161244, 725343385, 69407094565, 9639771895398, 1919182252611715, 541764452276876719, 214777343584048313318, 118575323291814379721651, 90492591258634595795504697, 94844885130660856889237907260, 135738086271526574073701454370969, 263921383510041055422284977248713291

Offset

0,1

Comments

Differs from A326878 in having a(0) = 2 instead of 1.

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = A000798(n) + A006058(n). - Jean-François Alcover, Dec 30 2019, after Gus Wiseman's comment in A006058.

Example

The a(0) = 2 through a(2) = 7 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}}

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n]]], Union@@#==Range[n]&&SubsetQ[#, Union[Union@@@Tuples[#, 2], Intersection@@@Tuples[#, 2]]]&]], {n, 0, 3}]
(* Second program: *)
A000798 = Cases[Import["https://oeis.org/A000798/b000798.txt", "Table"], {_, _}][[All, 2]];
A006058 = Cases[Import["https://oeis.org/A006058/b006058.txt", "Table"], {_, _}][[All, 2]];
a[n_] := A006058[[n + 1]] + A000798[[n + 1]];
a /@ Range[0, 18] (* Jean-François Alcover, Dec 30 2019 *)

Crossrefs

Covering sets of subsets are A000371.

The case without empty sets is A108798.

The case with a single covering edge is A326878.

The unlabeled version is A326898 for n > 0.

The case closed only under union is A326906.

The case closed only under intersection is (also) A326906.

Cf. A000798, A001930, A003465, A006058, A306445, A326876, A326882, A326907, A326908.

Sequence in context: A350019 A298440 A317808 * A343260 A246053 A345759

Adjacent sequences: A326906 A326907 A326908 * A326910 A326911 A326912

Keyword

nonn

Author

Gus Wiseman, Aug 04 2019

Extensions

a(18) from A000798+A006058 by Jean-François Alcover, Dec 30 2019

Status

approved