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 A326974 Number of unlabeled set-systems covering n vertices where every vertex is the unique common element of some subset of the edges, also called unlabeled covering T_1 set-systems. 17
 1, 1, 2, 16, 1212 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Alternatively, these are unlabeled set-systems covering n vertices whose dual is a (strict) antichain. A set-system is a finite set of finite nonempty sets. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. An antichain is a set-system where no edge is a subset of any other. LINKS FORMULA a(n > 0) = A326972(n) - A326972(n - 1). EXAMPLE Non-isomorphic representatives of the a(0) = 1 through a(3) = 16 set-systems:   {}  {{1}}  {{1},{2}}        {{1},{2},{3}}              {{1},{2},{1,2}}  {{1,2},{1,3},{2,3}}                               {{1},{2},{3},{2,3}}                               {{1},{2},{1,3},{2,3}}                               {{1},{2},{3},{1,2,3}}                               {{3},{1,2},{1,3},{2,3}}                               {{1},{2},{3},{1,3},{2,3}}                               {{1,2},{1,3},{2,3},{1,2,3}}                               {{1},{2},{3},{2,3},{1,2,3}}                               {{2},{3},{1,2},{1,3},{2,3}}                               {{1},{2},{1,3},{2,3},{1,2,3}}                               {{1},{2},{3},{1,2},{1,3},{2,3}}                               {{3},{1,2},{1,3},{2,3},{1,2,3}}                               {{1},{2},{3},{1,3},{2,3},{1,2,3}}                               {{2},{3},{1,2},{1,3},{2,3},{1,2,3}}                               {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}} CROSSREFS Unlabeled covers are A055621. The same with T_0 instead of T_1 is A319637. The labeled version is A326961. The non-covering version is A326972 (partial sums). Unlabeled covering set-systems whose dual is a weak antichain are A326973. Cf. A000612, A059523, A319559, A326946, A326951, A326965, A326970, A326971, A326976, A326977, A326979. Sequence in context: A002543 A125791 A102103 * A060597 A091479 A016031 Adjacent sequences:  A326971 A326972 A326973 * A326975 A326976 A326977 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 11 2019 STATUS approved

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Last modified February 24 00:38 EST 2020. Contains 332195 sequences. (Running on oeis4.)