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 A326277 Number of crossing normal multiset partitions of weight n. 1
 0, 0, 0, 0, 1, 22, 314, 3711, 39947 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A multiset partition is normal if it covers an initial interval of positive integers. A multiset partition is crossing if it has two blocks of the form {...x...y...}, {...z...t...} where x < z < y < t or z < x < t < y. LINKS EXAMPLE The a(5) = 22 crossing normal multiset partitions:   {{1,3},{1,2,4}}  {{1},{1,3},{2,4}}   {{1,3},{2,2,4}}  {{1},{2,4},{3,5}}   {{1,3},{2,3,4}}  {{2},{1,3},{2,4}}   {{1,3},{2,4,4}}  {{2},{1,4},{3,5}}   {{1,3},{2,4,5}}  {{3},{1,3},{2,4}}   {{1,4},{2,3,5}}  {{3},{1,4},{2,5}}   {{2,4},{1,1,3}}  {{4},{1,3},{2,4}}   {{2,4},{1,2,3}}  {{4},{1,3},{2,5}}   {{2,4},{1,3,3}}  {{5},{1,3},{2,4}}   {{2,4},{1,3,4}}   {{2,4},{1,3,5}}   {{2,5},{1,3,4}}   {{3,5},{1,2,4}} 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]]]]; allnorm[n_]:=If[n<=0, {{}}, Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]]; croXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x

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