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 A322112 Number of non-isomorphic self-dual connected multiset partitions of weight n with no singletons and multiset density -1. 1
 1, 0, 1, 1, 1, 2, 2, 4, 4, 9, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices. 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}}. A multiset partition is self-dual if it is isomorphic to its dual. For example, {{1,1},{1,2,2},{2,3,3}} is self-dual, as it is isomorphic to its dual {{1,1,2},{2,2,3},{3,3}}. The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. LINKS Table of n, a(n) for n=0..10. EXAMPLE Non-isomorphic representatives of the a(2) = 1 through a(10) = 9 multiset partitions: {{11}} {{111}} {{1111}} {{11111}} {{111111}} {{1111111}} {{11}{122}} {{22}{1122}} {{111}{1222}} {{22}{11222}} {{11}{12}{233}} . {{11111111}} {{111111111}} {{1111111111}} {{111}{11222}} {{1111}{12222}} {{1111}{112222}} {{22}{112222}} {{22}{1122222}} {{22}{11222222}} {{11}{122}{233}} {{222}{111222}} {{222}{1112222}} {{11}{11}{12233}} {{111}{122}{2333}} {{11}{113}{2233}} {{22}{113}{23333}} {{12}{111}{2333}} {{22}{1133}{2233}} {{22}{113}{2333}} {{33}{33}{112233}} {{12}{13}{22}{344}} {{11}{14}{223}{344}} CROSSREFS Cf. A000272, A007716, A007718, A030019, A052888, A134954, A304867, A304887, A316983, A321155, A321255, A322111. Sequence in context: A288045 A292941 A074818 * A324409 A110199 A358429 Adjacent sequences: A322109 A322110 A322111 * A322113 A322114 A322115 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 26 2018 STATUS approved

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Last modified August 10 16:09 EDT 2024. Contains 375057 sequences. (Running on oeis4.)