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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 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 April 2 02:53 EDT 2023. Contains 361723 sequences. (Running on oeis4.)