A326908 Number of non-isomorphic sets of subsets of {1..n} that are closed under union and intersection.

2, 4, 9, 23, 70, 256, 1160, 6599, 48017, 452518, 5574706, 90198548, 1919074899, 53620291147, 1962114118390, 93718030190126, 5822768063787557

Offset: 0

Author

Gus Wiseman, Aug 03 2019

Keywords

• nonn
• more

Examples

			Non-isomorphic representatives of the a(0) = 2 through a(3) = 23 sets of subsets:
  {}    {}       {}              {}
  {{}}  {{}}     {{}}            {{}}
        {{1}}    {{1}}           {{1}}
        {{}{1}}  {{12}}          {{12}}
                 {{}{1}}         {{}{1}}
                 {{}{12}}        {{123}}
                 {{2}{12}}       {{}{12}}
                 {{}{2}{12}}     {{}{123}}
                 {{}{1}{2}{12}}  {{2}{12}}
                                 {{3}{123}}
                                 {{}{2}{12}}
                                 {{23}{123}}
                                 {{}{3}{123}}
                                 {{}{23}{123}}
                                 {{}{1}{2}{12}}
                                 {{3}{23}{123}}
                                 {{}{1}{23}{123}}
                                 {{}{3}{23}{123}}
                                 {{3}{13}{23}{123}}
                                 {{}{2}{3}{23}{123}}
                                 {{}{3}{13}{23}{123}}
                                 {{}{2}{3}{13}{23}{123}}
                                 {{}{1}{2}{3}{12}{13}{23}{123}}
		

Crossrefs

The labeled version is A306445.

Taking first differences and prepending 1 gives A326898.

Taking second differences and prepending two 1's gives A001930.

Cf. A000612, A000798, A003180, A108798, A108800, A193675, A326867, A326876, A326878, A326882, A326883.

Programs

Mathematica

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