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A326908 Number of non-isomorphic sets of subsets of {1..n} that are closed under union and intersection. 4
2, 4, 9, 23, 70, 256, 1160, 6599, 48017, 452518, 5574706, 90198548, 1919074899, 53620291147, 1962114118390, 93718030190126, 5822768063787557 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..16.

EXAMPLE

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}}

MATHEMATICA

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

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.

Sequence in context: A125789 A058731 A291981 * A229048 A144309 A080376

Adjacent sequences:  A326905 A326906 A326907 * A326909 A326910 A326911

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 03 2019

STATUS

approved

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Last modified January 19 09:28 EST 2020. Contains 331048 sequences. (Running on oeis4.)