cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A320328 Number of square multiset partitions of integer partitions of n.

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%I A320328 #6 Oct 11 2018 10:10:10
%S A320328 1,1,2,3,6,11,20,36,65,117,214,382,679
%N A320328 Number of square multiset partitions of integer partitions of n.
%C A320328 A multiset partition is square if its length is equal to its number of distinct atoms.
%e A320328 The a(1) = 1 through a(6) = 20 square partitions:
%e A320328   {{1}}  {{2}}    {{3}}      {{4}}        {{5}}          {{6}}
%e A320328          {{1,1}}  {{1,1,1}}  {{2,2}}      {{1},{4}}      {{3,3}}
%e A320328                   {{1},{2}}  {{1},{3}}    {{2},{3}}      {{1},{5}}
%e A320328                              {{1,1,1,1}}  {{1},{1,3}}    {{2,2,2}}
%e A320328                              {{1},{1,2}}  {{1},{2,2}}    {{2},{4}}
%e A320328                              {{2},{1,1}}  {{2},{1,2}}    {{1},{1,4}}
%e A320328                                           {{3},{1,1}}    {{4},{1,1}}
%e A320328                                           {{1,1,1,1,1}}  {{1},{1,1,3}}
%e A320328                                           {{1},{1,1,2}}  {{1,1},{1,3}}
%e A320328                                           {{1,1},{1,2}}  {{1},{1,2,2}}
%e A320328                                           {{2},{1,1,1}}  {{1,1},{2,2}}
%e A320328                                                          {{1,2},{1,2}}
%e A320328                                                          {{1},{2},{3}}
%e A320328                                                          {{2},{1,1,2}}
%e A320328                                                          {{3},{1,1,1}}
%e A320328                                                          {{1,1,1,1,1,1}}
%e A320328                                                          {{1},{1,1,1,2}}
%e A320328                                                          {{1,1},{1,1,2}}
%e A320328                                                          {{1,2},{1,1,1}}
%e A320328                                                          {{2},{1,1,1,1}}
%t A320328 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A320328 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A320328 Table[Length[Select[Join@@mps/@IntegerPartitions[n],Length[#]==Length[Union@@#]&]],{n,8}]
%Y A320328 Cf. A000219, A001970, A047968, A050342, A089259, A141268, A261049, A289501, A305551, A316983, A319066, A319312, A319616, A320330, A320331.
%K A320328 nonn,more
%O A320328 0,3
%A A320328 _Gus Wiseman_, Oct 11 2018