A169974 Sum_{i=0..n} { 2^C(n,i) } - n.

2, 3, 6, 17, 96, 2111, 1114238, 68723671293, 1180735735906024030716, 170141183460507917357914971986913657851, 7237005577335553223087828975127304179197147198604070555943173844710572689402

Offset

0,1

Comments

Abstract simplicial complexes with n vertices for which all facets have the same dimension

Links

Table of n, a(n) for n=0..10.

Example

There are 20 abstract simplicial complexes with 3 vertices; of these, all facets are the same dimension except for the 3 consisting of a line and a point such as {{1,2}, {3}}, so a(3)=17.

Mathematica

Table[Sum[2^Binomial[n, i], {i, 0, n}]-n, {n, 0, 12}] (* Harvey P. Dale, Oct 29 2021 *)

Prog

(PARI) a(n) = sum(i=0, n, 2^binomial(n, i)) - n; \\ Michel Marcus, Aug 23 2013

Crossrefs

Cf. A000372(n) is the count over n vertices when we don't restrict to facets of the same dimension.

Sequence in context: A114491 A122939 A321399 * A003183 A213616 A359180

Adjacent sequences: A169971 A169972 A169973 * A169975 A169976 A169977

Keyword

easy,nonn

Author

Hugo van der Sanden, Aug 10 2010

Extensions

Edited by N. J. A. Sloane, Aug 10 2010

Status

approved