A317632 Number of connected induced nonempty non-singleton subgraphs of labeled connected graphs with n vertices.

0, 0, 1, 13, 294, 12198, 946712, 140168924, 40223263760, 22598607583376, 24999757695984960, 54630901092648916704, 236304498092496715916416, 2026201628540583716863002880, 34482826679730591694177065948928, 1166004710785628820717860509317415168

Offset

0,4

Comments

The edges of an induced subgraph G|S are those edges of G with both ends contained in S, where S is a subset of the vertices.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Gus Wiseman, All 294 connected induced subgraphs of labeled connected graphs with 4 vertices.

Prog

(PARI)
seq(n)={
  my(p=sum(k=0, n, 2^binomial(k, 2)*x^k/k!, O(x*x^n)));
  my(g=Vec(serlaplace(log(p))));
  my(q=sum(k=0, n, sum(j=2, k, binomial(k, j)*g[j]*2^(binomial(k-j, 2) + j*(k-j)))*x^k/k!, O(x*x^n)));
  Vec(serlaplace(q/p), -n-1)
} \\ Andrew Howroyd, Dec 10 2018

Crossrefs

Cf. A001187, A006125, A048143, A293510, A304717, A317631, A317634, A317635.

Sequence in context: A246462 A023357 A165218 * A076130 A035272 A296319

Adjacent sequences: A317629 A317630 A317631 * A317633 A317634 A317635

Keyword

nonn

Author

Gus Wiseman, Aug 02 2018

Extensions

a(6) from Gus Wiseman, Dec 10 2018

Terms a(7) and beyond from Andrew Howroyd, Dec 10 2018

Status

approved