A332872 - OEIS

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A332872

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.

1, 1, 3, 10, 34, 116, 396, 1352, 4616, 15760

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

After initial terms, first differs from A291292 at a(7) = 1352, A291292(8) = 1353.

Conjectured to be the same as A007052, shifted right once.

LINKS

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

EXAMPLE

The a(1) = 1 through a(3) = 10 ordered set partitions:

{{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}}

MATHEMATICA

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}]

CROSSREFS

Row sums of A332673.

Set partitions are A000110.

Ordered set-partitions are A000670.

Unimodal sequences covering an initial interval are A007052.

Cf. A001523, A056242, A097805, A328509, A332280, A332283, A332294, A332724.

Sequence in context: A291337 A255813 A113300 * A048580 A007052 A291292

Adjacent sequences: A332869 A332870 A332871 * A332873 A332874 A332875

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Mar 06 2020

STATUS

approved

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