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 A320331 Number of strict T_0 multiset partitions of integer partitions of n. 7
 1, 1, 2, 4, 8, 17, 30, 61, 110, 207, 381, 711, 1250 (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 T_0 condition means the dual is strict. LINKS Table of n, a(n) for n=0..12. EXAMPLE The a(1) = 1 through a(5) = 17 multiset partitions: {{1}} {{2}} {{3}} {{4}} {{5}} {{1,1}} {{1,1,1}} {{2,2}} {{1,1,3}} {{1},{2}} {{1,1,2}} {{1,2,2}} {{1},{1,1}} {{1},{3}} {{1},{4}} {{1,1,1,1}} {{2},{3}} {{1},{1,2}} {{1,1,1,2}} {{2},{1,1}} {{1},{1,3}} {{1},{1,1,1}} {{1},{2,2}} {{2},{1,2}} {{3},{1,1}} {{1,1,1,1,1}} {{1},{1,1,2}} {{1,1},{1,2}} {{2},{1,1,1}} {{1},{1,1,1,1}} {{1,1},{1,1,1}} {{1},{2},{1,1}} MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]]; dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}]; Table[Length[Select[Join@@mps/@IntegerPartitions[n], And[UnsameQ@@#, UnsameQ@@dual[#]]&]], {n, 8}] CROSSREFS Cf. A001970, A047968, A050342, A089259, A141268, A261049, A289501, A305551, A319066, A319312, A320328, A320330. Sequence in context: A342773 A080281 A172446 * A289322 A349842 A049962 Adjacent sequences: A320328 A320329 A320330 * A320332 A320333 A320334 KEYWORD nonn,more AUTHOR Gus Wiseman, Oct 11 2018 STATUS approved

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Last modified May 19 12:47 EDT 2024. Contains 372692 sequences. (Running on oeis4.)