%I #15 Jul 23 2024 20:34:34
%S 2,6,26,191,1904,22078,282388,3848001,54953996,814302292
%N Number of unrooted 3-regular planar maps with 2n vertices, up to orientation-preserving isomorphisms.
%C A 3-regular map is a regular map with valency 3.
%H Z. C. Gao, V. A. Liskovets and N. C. Wormald, <a href="http://mathstat.carleton.ca/~zgao/PAPER/poles.pdf">Enumeration of unrooted odd-valent regular planar maps</a>, Preprint, 2005.
%H Mark van Hoeij, Vijay Jung Kunwar, <a href="http://arxiv.org/abs/1604.08158">Classifying (near)-Belyi maps with Five Exceptional Points</a>, arXiv preprint arXiv:1604.08158, 2016. Also in <a href="https://doi.org/10.1016/j.indag.2018.09.003">Indagationes Mathematicae</a> (2019) Vol. 30, No. 1, 136-156.
%H Riccardo Murri, <a href="https://arxiv.org/abs/1202.1820">Fatgraph algorithms and the homology of the Kontsevich complex</a>, arXiv preprint arXiv:1202.1820, 2012.
%e 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.
%Y Cf. A112944, A112945, A112949 (5-regular), A005470.
%Y 3-regular maps on the torus: A292408.
%K nonn
%O 1,1
%A _Valery A. Liskovets_, Oct 10 2005