A327899 Number of set partitions of {1..n} with equal block sizes and equal block sums.

1, 1, 1, 1, 2, 1, 2, 1, 6, 3, 2, 1, 63, 1, 2, 317, 657, 1, 4333, 1, 9609

Offset

0,5

Links

Table of n, a(n) for n=0..20.

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

Example

The a(8) = 6 set partitions:
     {{1,2,3,4,5,6,7,8}}
    {{1,2,7,8},{3,4,5,6}}
    {{1,3,6,8},{2,4,5,7}}
    {{1,4,5,8},{2,3,6,7}}
    {{1,4,6,7},{2,3,5,8}}
  {{1,8},{2,7},{3,6},{4,5}}

Mathematica

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

Crossrefs

Set partitions with equal block-sizes are A038041.

Set partitions with equal block-sums are A035470.

Cf. A000110, A000258, A005651, A007837, A008277, A275780, A300335, A319189, A326512, A326513, A326515, A327908.

Sequence in context: A319118 A163820 A284465 * A276157 A169593 A057568

Adjacent sequences: A327896 A327897 A327898 * A327900 A327901 A327902

Keyword

nonn,more

Author

Gus Wiseman, Sep 29 2019

Status

approved