A326512 Number of set partitions of {1..n} where every block has the same average.

1, 1, 1, 2, 2, 5, 5, 18, 16, 75, 64, 405, 302, 2581, 1693, 19872

Offset

0,4

Links

Table of n, a(n) for n=0..15.

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(7) = 18 set partitions:
  {1}  {12}  {123}    {1234}    {12345}      {123456}      {1234567}
             {13}{2}  {14}{23}  {1245}{3}    {1256}{34}    {123567}{4}
                                {135}{24}    {1346}{25}    {12467}{35}
                                {15}{234}    {16}{2345}    {1267}{345}
                                {15}{24}{3}  {16}{25}{34}  {13457}{26}
                                                           {1357}{246}
                                                           {1456}{237}
                                                           {147}{2356}
                                                           {156}{2347}
                                                           {17}{23456}
                                                           {1267}{35}{4}
                                                           {1357}{26}{4}
                                                           {147}{26}{35}
                                                           {156}{237}{4}
                                                           {17}{2356}{4}
                                                           {17}{246}{35}
                                                           {17}{26}{345}
                                                           {17}{26}{35}{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]], SameQ@@Mean/@#&]], {n, 0, 8}]

Crossrefs

Cf. A000110, A007837, A035470, A038041, A275780, A306017, A306021, A319169, A326513, A326515, A326520, A326536.

Sequence in context: A245850 A245844 A083849 * A325983 A063501 A103892

Adjacent sequences: A326509 A326510 A326511 * A326513 A326514 A326515

Keyword

nonn,more

Author

Gus Wiseman, Jul 11 2019

Extensions

a(12)-a(15) from Alois P. Heinz, Jul 12 2019

Status

approved