This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326900 Number of set-systems on n vertices that are closed under union and intersection. 4
 1, 2, 6, 29, 232, 3032, 62837, 2009408, 97034882, 6952703663, 728107141058, 109978369078580, 23682049666957359, 7195441649260733390, 3056891748255795885338, 1801430622263459795017565 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A set-system is a finite set of finite nonempty sets, so no two edges of such a set-system can be disjoint. LINKS EXAMPLE The a(0) = 1 through a(3) = 29 set-systems:   {}  {}     {}           {}       {{1}}  {{1}}        {{1}}              {{2}}        {{2}}              {{1,2}}      {{3}}              {{1},{1,2}}  {{1,2}}              {{2},{1,2}}  {{1,3}}                           {{2,3}}                           {{1,2,3}}                           {{1},{1,2}}                           {{1},{1,3}}                           {{2},{1,2}}                           {{2},{2,3}}                           {{3},{1,3}}                           {{3},{2,3}}                           {{1},{1,2,3}}                           {{2},{1,2,3}}                           {{3},{1,2,3}}                           {{1,2},{1,2,3}}                           {{1,3},{1,2,3}}                           {{2,3},{1,2,3}}                           {{1},{1,2},{1,2,3}}                           {{1},{1,3},{1,2,3}}                           {{2},{1,2},{1,2,3}}                           {{2},{2,3},{1,2,3}}                           {{3},{1,3},{1,2,3}}                           {{3},{2,3},{1,2,3}}                           {{1},{1,2},{1,3},{1,2,3}}                           {{2},{1,2},{2,3},{1,2,3}}                           {{3},{1,3},{2,3},{1,2,3}} MATHEMATICA Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], SubsetQ[#, Union[Union@@@Tuples[#, 2], Intersection@@@Tuples[#, 2]]]&]], {n, 0, 3}] CROSSREFS Binomial transform of A006058 (the covering case). The case closed under union only is A102896. The case with {} allowed is A306445. The BII-numbers of these set-systems are A326876. The case closed under intersection only is A326901. The unlabeled version is A326908. Cf. A000798, A001930, A102895, A102898, A326866, A326878, A326882. Sequence in context: A321961 A088957 A030538 * A181812 A076978 A079615 Adjacent sequences:  A326897 A326898 A326899 * A326901 A326902 A326903 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 04 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)