A326908 - OEIS

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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

(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}} {{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