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

Author

Gus Wiseman, Aug 04 2019

Keywords

• nonn

Comments

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

Examples

			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}}
		

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.

Programs

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 *)

Formula

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

Extensions

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