This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326254 Number of non-capturing set partitions of {1..n}. 9
 1, 1, 2, 5, 14, 41, 123, 374, 1147, 3538, 10958, 34042, 105997 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Conjectured to be equal to A054391. A set partition is capturing if it has two blocks of the form {...x...y...} and {...z...t...} where x < z and y > t or x > z and y < t. Capturing is a weaker condition than nesting, so for example {{1,3,5},{2,4}} is capturing but not nesting. LINKS Eric Marberg, Crossings and nestings in colored set partitions, arXiv preprint arXiv:1203.5738 [math.CO], 2012. FORMULA a(n) = A000110(n) - A326243(n). EXAMPLE The a(0) = 1 through a(4) = 14 non-capturing set partitions:   {}  {{1}}  {{1,2}}    {{1,2,3}}      {{1,2,3,4}}              {{1},{2}}  {{1},{2,3}}    {{1},{2,3,4}}                         {{1,2},{3}}    {{1,2},{3,4}}                         {{1,3},{2}}    {{1,2,3},{4}}                         {{1},{2},{3}}  {{1,2,4},{3}}                                        {{1,3},{2,4}}                                        {{1,3,4},{2}}                                        {{1},{2},{3,4}}                                        {{1},{2,3},{4}}                                        {{1,2},{3},{4}}                                        {{1},{2,4},{3}}                                        {{1,3},{2},{4}}                                        {{1,4},{2},{3}}                                        {{1},{2},{3},{4}} MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; capXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; xt||x>z&&y

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.

Last modified September 22 05:47 EDT 2019. Contains 327287 sequences. (Running on oeis4.)