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 A319769 Number of non-isomorphic intersecting set multipartitions (multisets of sets) of weight n whose dual is also an intersecting set multipartition. 6
 1, 1, 2, 3, 5, 7, 12, 16, 26, 38, 61 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part. LINKS EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set multipartitions: 1: {{1}} 2: {{1,2}}    {{1},{1}} 3: {{1,2,3}}    {{2},{1,2}}    {{1},{1},{1}} 4: {{1,2,3,4}}    {{3},{1,2,3}}    {{1,2},{1,2}}    {{2},{2},{1,2}}    {{1},{1},{1},{1}} 5: {{1,2,3,4,5}}    {{4},{1,2,3,4}}    {{2,3},{1,2,3}}    {{2},{1,2},{1,2}}    {{3},{3},{1,2,3}}    {{2},{2},{2},{1,2}}    {{1},{1},{1},{1},{1}} CROSSREFS Cf. A007716, A281116, A283877, A305854, A306006,  A316980, A316983, A317757, A319616. Cf. A319752, A319765, A319766, A319767, A319768, A319773, A319774. Sequence in context: A275592 A319635 A179822 * A326083 A027959 A060730 Adjacent sequences:  A319766 A319767 A319768 * A319770 A319771 A319772 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 27 2018 STATUS approved

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Last modified December 14 17:41 EST 2019. Contains 329979 sequences. (Running on oeis4.)