The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #29 Mar 11 2023 05:10:35
%S 1,3,7,30,124,733,4586,33373,259434,2152298,18615182,166544071,
%T 1528659536,14328433429,136649176084,1322594487342,12965736092988,
%U 128543259338048
%N Number of isomorphism classes of connected plane 4-regular multigraphs.
%C Previous name was: Number of link shadows with n crossings.
%C A link shadow is a connected plane 4-regular multigraph, allowing loops and multiple edges. Also: number of plane quadrangulations (allowing multiple edges) with n+2 vertices. In each case the sequence counts isomorphism classes which respect the embedding, with mirror image being an isomorphism. - _Brendan McKay_, Mar 10 2023
%H J. Cantarella, H. Chapman, and M. Mastin, <a href="https://arxiv.org/abs/1512.05749">Knot Probabilities in Random Diagrams</a>, arXiv preprint arXiv:1512.05749 [math.GT], 2015. See Tables 1.
%H Richard Kapolnai, Gabor Domokos, and Timea Szabo, <a href="http://dx.doi.org/10.3311/PPee.7074">Generating spherical multiquadrangulations by restricted vertex splittings and the reducibility of equilibrium classes</a>, Periodica Polytechnica Electrical Engineering, 56(1):11-10, 2012. Also arXiv:1206.1698, 2012.
%e a(1)=1 corresponds to a single vertex with two loops. a(2)=3 corresponds to two vertices joined by 4 edges or two vertices with loops joined by 2 edges. In the last case, the two loops may lie in the same face or different faces and these are not isomorphic.
%Y A054935 is the same but not allowing mirror image as an isomorphism.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_, Nov 07 2016
%E a(11)-a(18) from Heidi Van den Camp and _Brendan McKay_, Mar 10 2023