A326513 Number of set partitions of {1..n} where each block has a different average.

1, 1, 2, 4, 12, 40, 154, 650, 3024, 15110, 81538, 468494, 2863340

Offset

0,3

Links

Table of n, a(n) for n=0..12.

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

Example

The a(1) = 1 through a(4) = 12 set partitions:
  {{1}}  {{1,2}}    {{1,2,3}}      {{1,2,3,4}}
         {{1},{2}}  {{1},{2,3}}    {{1},{2,3,4}}
                    {{1,2},{3}}    {{1,2},{3,4}}
                    {{1},{2},{3}}  {{1,2,3},{4}}
                                   {{1,2,4},{3}}
                                   {{1,3},{2,4}}
                                   {{1,3,4},{2}}
                                   {{1},{2},{3,4}}
                                   {{1},{2,3},{4}}
                                   {{1,2},{3},{4}}
                                   {{1,4},{2},{3}}
                                   {{1},{2},{3},{4}}

Mathematica

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Select[sps[Range[n]], UnsameQ@@Mean/@#&]], {n, 0, 8}]

Crossrefs

Cf. A000110, A007837, A035470, A038041, A275780, A326512, A326516, A326521, A326537.

Sequence in context: A074034 A268952 A215072 * A268953 A268954 A268955

Adjacent sequences: A326510 A326511 A326512 * A326514 A326515 A326516

Keyword

nonn,more

Author

Gus Wiseman, Jul 11 2019

Extensions

a(12) from Alois P. Heinz, Jul 12 2019

Status

approved