A112949 -id:A112949 - cp's OEIS frontend

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

Valery A. Liskovets, Oct 10 2005

nonn

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

			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.

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.

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

3-regular maps on the torus: A292408.

A112950 Number of unrooted regular planar maps of valency 7 with 2n vertices (considered up to orientation-preserving homeomorphisms).

Original entry on oeis.org

39, 80600, 513654400, 4742588317460, 53786496621600480, 696401295433093120200, 9891028759926839453714800, 150420303869075439022288355100, 2410984386008752279281147366400400

Offset: 1

Valery A. Liskovets, Oct 10 2005

nonn

No closed formula is known.

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

Cf. A112949.

cp's OEIS Frontend

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

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