A324011 - OEIS

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A324011

Number of set partitions of {1, ..., n} with no singletons or cyclical adjacencies (successive elements in the same block, where 1 is a successor of n).

1, 0, 0, 0, 1, 0, 5, 14, 66, 307, 1554, 8415, 48530, 296582, 1913561, 12988776, 92467629, 688528288, 5349409512, 43270425827, 363680219762, 3170394634443, 28619600156344, 267129951788160, 2574517930001445, 25587989366964056, 261961602231869825

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OFFSET

0,7

COMMENTS

These set partitions are fixed points under Callan's bijection phi on set partitions.

LINKS

Table of n, a(n) for n=0..26.

David Callan, On conjugates for set partitions and integer compositions, arXiv:math/0508052 [math.CO], 2005.

EXAMPLE

The a(4) = 1, a(6) = 5, and a(7) = 14 set partitions:

{{13}{24}} {{135}{246}} {{13}{246}{57}}

{{13}{25}{46}} {{13}{257}{46}}

{{14}{25}{36}} {{135}{26}{47}}

{{14}{26}{35}} {{135}{27}{46}}

{{15}{24}{36}} {{136}{24}{57}}

{{136}{25}{47}}

{{14}{257}{36}}

{{14}{26}{357}}

{{146}{25}{37}}

{{146}{27}{35}}

{{15}{246}{37}}

{{15}{247}{36}}

{{16}{24}{357}}

{{16}{247}{35}}

MATHEMATICA

Table[Select[sps[Range[n]], And[Count[#, {_}]==0, Total[If[First[#]==1&&Last[#]==n, 1, 0]+Count[Subtract@@@Partition[#, 2, 1], -1]&/@#]==0]&]//Length, {n, 0, 10}]

CROSSREFS

Cf. A000110, A000126, A000296 (singletons allowed, or adjacencies allowed), A001610, A124323, A169985, A261139, A324012, A324014, A324015.

Sequence in context: A004030 A256413 A346212 * A194994 A166795 A128102

Adjacent sequences: A324008 A324009 A324010 * A324012 A324013 A324014

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 12 2019

EXTENSIONS

a(11)-a(26) from Alois P. Heinz, Feb 12 2019

STATUS

approved