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A326518 Number of normal multiset partitions of weight n where every part has the same sum. 13
1, 1, 3, 7, 15, 31, 75, 169, 445, 1199 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A multiset partition is normal if it covers an initial interval of positive integers.

LINKS

Table of n, a(n) for n=0..9.

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

EXAMPLE

The a(0) = 1 through a(4) = 15 normal multiset partitions:

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

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

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

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

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

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

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

{{1,2,3,4}}

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

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

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

{{1,4},{2,3}}

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

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

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

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]]]];

allnorm[n_]:=If[n<=0, {{}}, Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]];

Table[Length[Select[Join@@mps/@allnorm[n], SameQ@@Total/@#&]], {n, 0, 5}]

CROSSREFS

Cf. A035470, A038041, A255906, A317583, A321455, A326517, A326519, A326520, A326521, A326534.

Sequence in context: A024876 A146598 A147094 * A147285 A147250 A336701

Adjacent sequences: A326515 A326516 A326517 * A326519 A326520 A326521

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 12 2019

STATUS

approved

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Last modified February 2 16:46 EST 2023. Contains 360023 sequences. (Running on oeis4.)