A394755 Number of connected semi-bipartite structures on n unlabeled vertices.

0, 0, 1, 4, 18, 111, 948, 12117, 248598, 8729910, 546656296, 62211632285, 12971518524320, 4978986704302097, 3532978161315634913, 4653469892186977002460, 11423275400784921191855736, 52462085466397337031539370710, 452380601683401136290499567383958

Offset

0,4

Comments

A semi-bipartite structure is a triple (G,U,V) such that G is a simple graph, U and V form a partition of V[G], and U is isolated in G. a(n) counts non-isomorphic triples (G,U,V) on n unlabeled vertices such that G is connected.

Since U and V form a partition, both must be nonempty. When U or V can be empty, the corresponding sequence is A394610.

When G isn't required to be connected, the corresponding sequence is A394754.

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = A394610(n) - A001349(n) for n>=2.

Example

For n = 3: a(2)=1 with the following structure: two connected vertices with one in U and the other in V.

Crossrefs

Cf. A394610, A001349, A394754.

Sequence in context: A144085 A375604 A003708 * A327679 A330353 A000986

Adjacent sequences: A394752 A394753 A394754 * A394756 A394757 A394758

Keyword

nonn

Author

Piotr Mitosek, Mar 31 2026

Status

approved