login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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). 12
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 (list; graph; refs; listen; history; text; internal format)
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: A197661 A004030 A256413 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 24 09:40 EST 2020. Contains 332209 sequences. (Running on oeis4.)