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, 18481390, 125838194, 897725927, 6715102246, 52372397021, 425716871241, 3594451206166, 31509992921241, 285799247349838, 2682935185643622, 25990339824995969, 259777696236210943, 2673388551328088666

Offset

0,3

Links

Table of n, a(n) for n=0..25.

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

Author

Gus Wiseman, Jul 11 2019

Extensions

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

a(13)-a(25) from Christian Sievers, Aug 20 2024

Status

approved