A111757 Number of bipartite 2-connected outerplanar graphs on n unlabeled nodes.

0, 1, 0, 1, 0, 2, 0, 4, 0, 13, 0, 48, 0, 238, 0, 1325, 0, 8297, 0, 54519, 0, 373363, 0, 2621872, 0, 18797682, 0, 136969519, 0, 1011903735, 0, 7564219361, 0, 57129086391, 0, 435394899361, 0, 3345082819597, 0, 25885718422329, 0, 201619294539406, 0, 1579629974876090

Offset: 1

Author

Stefan Vigerske, Nov 21 2005

Keywords

• nonn

Comments

Also the number of bipartite (unlabeled) dissections of a polygon.

Links

• M. Bordirsky, É. Fusy, M. Kang and S. Vigerske, Enumeration of Unlabeled Outerplanar Graphs, 2005
• S. Vigerske, Asymptotic enumeration of unlabeled outerplanar graphs, Diploma thesis, Humboldt University Berlin, 2005
• S. Vigerske, Homepage

Crossrefs

Even bisection gives A290722.

Cf. A001004, A111758, A111759, A295419.

Programs

PARI

\\ See A295419 for DissectionsModDihedral.
{my(N=50); DissectionsModDihedral(vector(N, n, n%2==0)) + vector(N, n, n==2)} \\ Andrew Howroyd, Feb 12 2021

Formula

Generating function and cycle index sum known, see Vigerske.

Extensions

Terms a(21) and beyond from Andrew Howroyd, Feb 12 2021