login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317584 Number of multiset partitions of strongly normal multisets of size n such that all blocks have the same size. 3
1, 4, 6, 19, 14, 113, 30, 584 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities.

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

The a(4) = 19 multiset partitions:

  {{1,1,1,1}}, {{1,1},{1,1}}, {{1},{1},{1},{1}},

  {{1,1,1,2}}, {{1,1},{1,2}}, {{1},{1},{1},{2}},

  {{1,1,2,2}}, {{1,1},{2,2}}, {{1,2},{1,2}}, {{1},{1},{2},{2}},

  {{1,1,2,3}}, {{1,1},{2,3}}, {{1,2},{1,3}}, {{1},{1},{2},{3}},

  {{1,2,3,4}}, {{1,2},{3,4}}, {{1,3},{2,4}}, {{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, ___}];

mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];

strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n];

Table[Length[Select[Join@@mps/@strnorm[n], SameQ@@Length/@#&]], {n, 6}]

CROSSREFS

Cf. A000005, A007716, A038041, A255906, A298422, A306017, A306018, A306019, A306020, A306021, A317583.

Sequence in context: A057393 A196570 A274992 * A012928 A013160 A153777

Adjacent sequences:  A317581 A317582 A317583 * A317585 A317586 A317587

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 01 2018

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 July 22 02:26 EDT 2019. Contains 325210 sequences. (Running on oeis4.)