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 A326211 Number of unsortable normal multiset partitions of weight n. 18
 0, 0, 0, 1, 17, 170, 1455, 11678, 92871, 752473 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS A multiset partition is normal if it covers an initial interval of positive integers. It is unsortable if no permutation has an ordered concatenation, or equivalently if the concatenation of its lexicographically-ordered parts is not weakly increasing. For example, the multiset partition {{1,2},{1,1,1},{2,2,2}} is sortable because the permutation ((1,1,1),(1,2),(2,2,2)) has concatenation (1,1,1,1,2,2,2,2), which is weakly increasing. LINKS FORMULA A255906(n) = a(n) + A326212(n). EXAMPLE The a(3) = 1 and a(4) = 17 multiset partitions:   {{1,3},{2}}  {{1,1,3},{2}}                {{1,2},{1,2}}                {{1,2},{1,3}}                {{1,2,3},{2}}                {{1,2,4},{3}}                {{1,3},{2,2}}                {{1,3},{2,3}}                {{1,3},{2,4}}                {{1,3,3},{2}}                {{1,3,4},{2}}                {{1,4},{2,3}}                {{1},{1,3},{2}}                {{1},{2,4},{3}}                {{1,3},{2},{2}}                {{1,3},{2},{3}}                {{1,3},{2},{4}}                {{1,4},{2},{3}} MATHEMATICA lexsort[f_, c_]:=OrderedQ[PadRight[{f, c}]]; allnorm[n_]:=If[n<=0, {{}}, Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]]; 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]]]]; Table[Length[Select[Sort[#, lexsort]&/@Join@@mps/@allnorm[n], !OrderedQ[Join@@#]&]], {n, 0, 5}] CROSSREFS Unsortable set partitions are A058681. Sortable normal multiset partitions are A326212. Non-crossing normal multiset partitions are A324171. MM-numbers of unsortable multiset partitions are A326258. Cf. A000108, A016098, A255906, A324170. Cf. A326209, A326210, A326243, A326250, A326255, A326256. Sequence in context: A282922 A023015 A022645 * A119273 A164747 A166579 Adjacent sequences:  A326208 A326209 A326210 * A326212 A326213 A326214 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 19 2019 STATUS approved

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)