login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326335 Number of set partitions of {1..n} whose nesting blocks are connected. 5
1, 1, 1, 1, 2, 6, 21, 86, 394, 1974, 10696 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Two blocks are nesting if they are of the form {...x,y...}, {...z,t...} where x < z < t < y or z < x < y < t. A set partition has its nesting blocks connected if the graph whose vertices are the blocks and whose edges are nesting pairs of blocks is connected.
LINKS
EXAMPLE
The a(0) = 1 through a(6) = 21 set partitions:
{} {1} {12} {123} {1234} {12345} {123456}
{14}{23} {125}{34} {1236}{45}
{134}{25} {1245}{36}
{14}{235} {125}{346}
{145}{23} {1256}{34}
{15}{234} {126}{345}
{134}{256}
{1345}{26}
{1346}{25}
{136}{245}
{14}{2356}
{145}{236}
{1456}{23}
{146}{235}
{15}{2346}
{156}{234}
{16}{2345}
{15}{26}{34}
{16}{23}{45}
{16}{24}{35}
{16}{25}{34}
MATHEMATICA
nesXQ[stn_]:=MatchQ[stn, {___, {___, x_, y_, ___}, ___, {___, z_, t_, ___}, ___}/; x<z<t<y||z<x<y<t];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
nestcmpts[stn_]:=csm[Union[List/@stn, Select[Subsets[stn, {2}], nesXQ]]];
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Select[sps[Range[n]], Length[nestcmpts[#]]<=1&]], {n, 0, 5}]
CROSSREFS
Simple graphs whose nesting blocks are connected are A326330.
Set partitions whose crossing blocks are connected are A099947.
Set partitions whose capturing blocks are connected are A326336.
Sequence in context: A344229 A090805 A150226 * A256180 A150227 A263852
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 27 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 23:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)