A261005 Number of unlabeled simplicial complexes with n nodes.

1, 1, 2, 5, 20, 180, 16143, 489996795, 1392195548399980210, 789204635842035039135545297410259322

Offset

0,3

Comments

Also the number of non-isomorphic antichains of nonempty sets covering n vertices. The labeled case is A006126, except with a(0) = 1. - Gus Wiseman, Feb 23 2019

References

Benoît Jubin, Posting to Sequence Fans Mailing List, Aug 12 2015.

Links

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

C. Lienkaemper, A. Shiu, and Z. Woodstock, Obstructions to convexity in neural codes, Preprint 2015.

Francisco Ponce Carrión and Seth Sullivant, Marginal Independence and Partial Set Partitions, arXiv:2402.16292 [math.ST], 2024. See p. 21.

Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Formula

First differences of A306505. - Gus Wiseman, Feb 23 2019

a(n) = A003182(n) - A003182(n-1) for n > 0. - Andrew Howroyd, May 28 2023

Example

From Gus Wiseman, Feb 23 2019: (Start)
Non-isomorphic representatives of the a(0) = 1 through a(4) = 20 antichains:
  {}  {{1}}  {{12}}    {{123}}         {{1234}}
             {{1}{2}}  {{1}{23}}       {{1}{234}}
                       {{13}{23}}      {{12}{34}}
                       {{1}{2}{3}}     {{14}{234}}
                       {{12}{13}{23}}  {{1}{2}{34}}
                                       {{134}{234}}
                                       {{1}{24}{34}}
                                       {{1}{2}{3}{4}}
                                       {{13}{24}{34}}
                                       {{14}{24}{34}}
                                       {{13}{14}{234}}
                                       {{12}{134}{234}}
                                       {{1}{23}{24}{34}}
                                       {{124}{134}{234}}
                                       {{12}{13}{24}{34}}
                                       {{14}{23}{24}{34}}
                                       {{12}{13}{14}{234}}
                                       {{123}{124}{134}{234}}
                                       {{13}{14}{23}{24}{34}}
                                       {{12}{13}{14}{23}{24}{34}}
(End)

Crossrefs

Apart from a(0), same as A006602, and after subtracting 1, A007411.

Cf. A000372, A003182, A006126, A014466, A261006, A304997, A304998, A306505, A306550, A321679.

Sequence in context: A156871 A058109 A005331 * A158872 A308522 A216462

Adjacent sequences: A261002 A261003 A261004 * A261006 A261007 A261008

Keyword

nonn

Author

N. J. A. Sloane, Aug 13 2015

Extensions

a(8)-a(9) added using A003182 by Andrew Howroyd, May 28 2023

Status

approved