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

Author

Gus Wiseman, Aug 02 2018

Keywords

• nonn

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.

Crossrefs

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

Programs

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

Extensions

a(6) from Gus Wiseman, Dec 10 2018

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