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 A317078 Number of connected multiset partitions of strongly normal multisets of size n. 7
 1, 1, 3, 6, 18, 46, 172, 563, 2347 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities. LINKS EXAMPLE The a(3) = 6 connected multiset partitions are (111), (1)(11), (1)(1)(1), (112), (1)(12), (123). 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]]]]; csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], multijoin@@s[[c[[1]]]]]]]]]; strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n]; Length/@Table[Join@@Table[Select[mps[m], Length[csm[#]]==1&], {m, strnorm[n]}], {n, 8}] CROSSREFS Cf. A007716, A007718, A048143, A293994, A303837, A303838, A304716, A305078. Cf. A317074, A317076, A317077, A317080. Sequence in context: A032120 A115344 A223044 * A289587 A151262 A148555 Adjacent sequences:  A317075 A317076 A317077 * A317079 A317080 A317081 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 20 2018 STATUS approved

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)