A112948 Number of unrooted 3-regular planar maps with 2n vertices, up to orientation-preserving isomorphisms.

2, 6, 26, 191, 1904, 22078, 282388, 3848001, 54953996, 814302292

Offset

1,1

Comments

A 3-regular map is a regular map with valency 3.

Links

Table of n, a(n) for n=1..10.

Z. C. Gao, V. A. Liskovets and N. C. Wormald, Enumeration of unrooted odd-valent regular planar maps, Preprint, 2005.

Mark van Hoeij, Vijay Jung Kunwar, Classifying (near)-Belyi maps with Five Exceptional Points, arXiv preprint arXiv:1604.08158, 2016. Also in Indagationes Mathematicae (2019) Vol. 30, No. 1, 136-156.

Riccardo Murri, Fatgraph algorithms and the homology of the Kontsevich complex, arXiv preprint arXiv:1202.1820, 2012.

Example

There exist 2 planar maps with two 3-valent vertices: a map with three parallel edges and a map with one loop in each vertex and a link connecting the vertices. Therefore a(1)=2.

Crossrefs

Cf. A112944, A112945, A112949 (5-regular), A005470.

3-regular maps on the torus: A292408.

Sequence in context: A355211 A211604 A032014 * A007139 A306147 A331937

Adjacent sequences: A112945 A112946 A112947 * A112949 A112950 A112951

Keyword

nonn

Author

Valery A. Liskovets, Oct 10 2005

Status

approved