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A332872
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Number of ordered set partitions of {1..n} where no element of any block is greater than any element of a non-adjacent consecutive block.
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9
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OFFSET
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0,3
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COMMENTS
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After initial terms, first differs from A291292 at a(7) = 1352, A291292(8) = 1353.
Conjectured to be the same as A007052, shifted right once.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(3) = 10 ordered set partitions:
{{1}} {{1,2}} {{1,2,3}}
{{1},{2}} {{1},{2,3}}
{{2},{1}} {{1,2},{3}}
{{1,3},{2}}
{{2},{1,3}}
{{2,3},{1}}
{{3},{1,2}}
{{1},{2},{3}}
{{1},{3},{2}}
{{2},{1},{3}}
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MATHEMATICA
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sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Select[Join@@Permutations/@sps[Range[n]], !MatchQ[#, {___, {___, a_, ___}, __, {___, b_, ___}, ___}/; a>b]&]], {n, 0, 5}]
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CROSSREFS
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Ordered set-partitions are A000670.
Unimodal sequences covering an initial interval are A007052.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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