A326521 Number of normal multiset partitions of weight n where each part has a different average.

1, 1, 3, 11, 49, 251, 1418, 8904

Offset: 0

Author

Gus Wiseman, Jul 12 2019

Keywords

• nonn
• more

Comments

A multiset partition is normal if it covers an initial interval of positive integers.

Examples

			The a(0) = 1 through a(3) = 11 normal multiset partitions where each part has a different average:
  {}  {{1}}  {{1,1}}    {{1,1,1}}
             {{1,2}}    {{1,1,2}}
             {{1},{2}}  {{1,2,2}}
                        {{1,2,3}}
                        {{1},{1,2}}
                        {{1},{2,2}}
                        {{1},{2,3}}
                        {{2},{1,1}}
                        {{2},{1,2}}
                        {{3},{1,2}}
                        {{1},{2},{3}}
		

Links

• Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

Crossrefs

Cf. A051293, A255906, A317583, A326513, A326516, A326517, A326518, A326519, A326520, A326537.

Programs

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]]]];
allnorm[n_]:=If[n<=0,{{}},Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1]];
Table[Length[Select[Join@@mps/@allnorm[n],UnsameQ@@Mean/@#&]],{n,0,5}]