A394755 - OEIS

%I #12 Apr 07 2026 00:48:05

%S 0,0,1,4,18,111,948,12117,248598,8729910,546656296,62211632285,

%T 12971518524320,4978986704302097,3532978161315634913,

%U 4653469892186977002460,11423275400784921191855736,52462085466397337031539370710,452380601683401136290499567383958

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

%C 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.

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

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

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

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

%Y Cf. A394610, A001349, A394754.

%K nonn

%O 0,4

%A _Piotr Mitosek_, Mar 31 2026