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 A320328 Number of square multiset partitions of integer partitions of n. 12
 1, 1, 2, 3, 6, 11, 20, 36, 65, 117, 214, 382, 679 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A multiset partition is square if its length is equal to its number of distinct atoms. LINKS EXAMPLE The a(1) = 1 through a(6) = 20 square partitions:   {{1}}  {{2}}    {{3}}      {{4}}        {{5}}          {{6}}          {{1,1}}  {{1,1,1}}  {{2,2}}      {{1},{4}}      {{3,3}}                   {{1},{2}}  {{1},{3}}    {{2},{3}}      {{1},{5}}                              {{1,1,1,1}}  {{1},{1,3}}    {{2,2,2}}                              {{1},{1,2}}  {{1},{2,2}}    {{2},{4}}                              {{2},{1,1}}  {{2},{1,2}}    {{1},{1,4}}                                           {{3},{1,1}}    {{4},{1,1}}                                           {{1,1,1,1,1}}  {{1},{1,1,3}}                                           {{1},{1,1,2}}  {{1,1},{1,3}}                                           {{1,1},{1,2}}  {{1},{1,2,2}}                                           {{2},{1,1,1}}  {{1,1},{2,2}}                                                          {{1,2},{1,2}}                                                          {{1},{2},{3}}                                                          {{2},{1,1,2}}                                                          {{3},{1,1,1}}                                                          {{1,1,1,1,1,1}}                                                          {{1},{1,1,1,2}}                                                          {{1,1},{1,1,2}}                                                          {{1,2},{1,1,1}}                                                          {{2},{1,1,1,1}} 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]]]]; Table[Length[Select[Join@@mps/@IntegerPartitions[n], Length[#]==Length[Union@@#]&]], {n, 8}] CROSSREFS Cf. A000219, A001970, A047968, A050342, A089259, A141268, A261049, A289501, A305551, A316983, A319066, A319312, A319616, A320330, A320331. Sequence in context: A002985 A239342 A093608 * A079976 A017992 A018172 Adjacent sequences:  A320325 A320326 A320327 * A320329 A320330 A320331 KEYWORD nonn,more AUTHOR Gus Wiseman, Oct 11 2018 STATUS approved

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Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)