A326908 - OEIS

%I #4 Aug 04 2019 19:10:43

%S 2,4,9,23,70,256,1160,6599,48017,452518,5574706,90198548,1919074899,

%T 53620291147,1962114118390,93718030190126,5822768063787557

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

%e Non-isomorphic representatives of the a(0) = 2 through a(3) = 23 sets of subsets:

%e   {}    {}       {}              {}

%e   {{}}  {{}}     {{}}            {{}}

%e         {{1}}    {{1}}           {{1}}

%e         {{}{1}}  {{12}}          {{12}}

%e                  {{}{1}}         {{}{1}}

%e                  {{}{12}}        {{123}}

%e                  {{2}{12}}       {{}{12}}

%e                  {{}{2}{12}}     {{}{123}}

%e                  {{}{1}{2}{12}}  {{2}{12}}

%e                                  {{3}{123}}

%e                                  {{}{2}{12}}

%e                                  {{23}{123}}

%e                                  {{}{3}{123}}

%e                                  {{}{23}{123}}

%e                                  {{}{1}{2}{12}}

%e                                  {{3}{23}{123}}

%e                                  {{}{1}{23}{123}}

%e                                  {{}{3}{23}{123}}

%e                                  {{3}{13}{23}{123}}

%e                                  {{}{2}{3}{23}{123}}

%e                                  {{}{3}{13}{23}{123}}

%e                                  {{}{2}{3}{13}{23}{123}}

%e                                  {{}{1}{2}{3}{12}{13}{23}{123}}

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

%Y The labeled version is A306445.

%Y Taking first differences and prepending 1 gives A326898.

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

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

%K nonn,more

%O 0,1

%A _Gus Wiseman_, Aug 03 2019