login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326512 Number of set partitions of {1..n} where every block has the same average. 8
1, 1, 1, 2, 2, 5, 5, 18, 16, 75, 64, 405, 302, 2581, 1693, 19872 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)