cp's OEIS Frontend

A261005 Number of unlabeled simplicial complexes with n nodes.

%I A261005 #24 Mar 01 2024 01:59:55
%S A261005 1,1,2,5,20,180,16143,489996795,1392195548399980210,
%T A261005 789204635842035039135545297410259322
%N A261005 Number of unlabeled simplicial complexes with n nodes.
%C A261005 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
%D A261005 Benoît Jubin, Posting to Sequence Fans Mailing List, Aug 12 2015.
%H A261005 C. Lienkaemper, A. Shiu, and Z. Woodstock, <a href="http://www.math.tamu.edu/~annejls/papers/obstructions-convexity-neural.pdf">Obstructions to convexity in neural codes</a>, Preprint 2015.
%H A261005 Francisco Ponce Carrión and Seth Sullivant, <a href="https://arxiv.org/abs/2402.16292">Marginal Independence and Partial Set Partitions</a>, arXiv:2402.16292 [math.ST], 2024. See p. 21.
%H A261005 Gus Wiseman, <a href="/A048143/a048143_4.txt">Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons</a>.
%F A261005 First differences of A306505. - _Gus Wiseman_, Feb 23 2019
%F A261005 a(n) = A003182(n) - A003182(n-1) for n > 0. - _Andrew Howroyd_, May 28 2023
%e A261005 From _Gus Wiseman_, Feb 23 2019: (Start)
%e A261005 Non-isomorphic representatives of the a(0) = 1 through a(4) = 20 antichains:
%e A261005   {}  {{1}}  {{12}}    {{123}}         {{1234}}
%e A261005              {{1}{2}}  {{1}{23}}       {{1}{234}}
%e A261005                        {{13}{23}}      {{12}{34}}
%e A261005                        {{1}{2}{3}}     {{14}{234}}
%e A261005                        {{12}{13}{23}}  {{1}{2}{34}}
%e A261005                                        {{134}{234}}
%e A261005                                        {{1}{24}{34}}
%e A261005                                        {{1}{2}{3}{4}}
%e A261005                                        {{13}{24}{34}}
%e A261005                                        {{14}{24}{34}}
%e A261005                                        {{13}{14}{234}}
%e A261005                                        {{12}{134}{234}}
%e A261005                                        {{1}{23}{24}{34}}
%e A261005                                        {{124}{134}{234}}
%e A261005                                        {{12}{13}{24}{34}}
%e A261005                                        {{14}{23}{24}{34}}
%e A261005                                        {{12}{13}{14}{234}}
%e A261005                                        {{123}{124}{134}{234}}
%e A261005                                        {{13}{14}{23}{24}{34}}
%e A261005                                        {{12}{13}{14}{23}{24}{34}}
%e A261005 (End)
%Y A261005 Apart from a(0), same as A006602, and after subtracting 1, A007411.
%Y A261005 Cf. A000372, A003182, A006126, A014466, A261006, A304997, A304998, A306505, A306550, A321679.
%K A261005 nonn
%O A261005 0,3
%A A261005 _N. J. A. Sloane_, Aug 13 2015
%E A261005 a(8)-a(9) added using A003182 by _Andrew Howroyd_, May 28 2023