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A307249 Number of simplicial complexes with n nodes. 32
1, 1, 2, 9, 114, 6894, 7785062, 2414627396434, 56130437209370320359966 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Except for a(0) = 1, this is also the number of antichains of nonempty sets covering n vertices (A006126). There are two antichains of size zero, namely {} and {{}}, while there is only one simplicial complex, namely {}. The unlabeled case is A261005. The non-covering case is A014466.

LINKS

Table of n, a(n) for n=0..8.

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

FORMULA

Inverse binomial transform of A014466.

EXAMPLE

Maximal simplices of the a(0) = 1 through a(3) = 9 simplicial complexes:

  {}    {{1}}  {{12}}    {{123}}

               {{1}{2}}  {{1}{23}}

                         {{2}{13}}

                         {{3}{12}}

                         {{12}{13}}

                         {{12}{23}}

                         {{13}{23}}

                         {{1}{2}{3}}

                         {{12}{13}{23}}

MATHEMATICA

nn=5;

stableSets[u_, Q_]:=If[Length[u]===0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r===w||Q[r, w]||Q[w, r]], Q]]]];

Table[Length[stableSets[Subsets[Range[n], {2, n}], SubsetQ]], {n, 0, nn}]

CROSSREFS

Cf. A000372, A003182, A006126, A006602, A014466, A261005, A293606, A293993, A305000, A305844, A306550, A317674, A319721, A320449.

Sequence in context: A337043 A008269 A039718 * A201381 A075538 A067965

Adjacent sequences:  A307246 A307247 A307248 * A307250 A307251 A307252

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Mar 31 2019

STATUS

approved

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Last modified November 27 05:27 EST 2020. Contains 338678 sequences. (Running on oeis4.)