A277739 Number of isomorphism classes of connected plane 4-regular multigraphs.

1, 3, 7, 30, 124, 733, 4586, 33373, 259434, 2152298, 18615182, 166544071, 1528659536, 14328433429, 136649176084, 1322594487342, 12965736092988, 128543259338048

Offset: 1

Author

N. J. A. Sloane, Nov 07 2016

Keywords

• nonn
• more

Comments

Previous name was: Number of link shadows with n crossings.

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

Examples

			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.
		

Links

• J. Cantarella, H. Chapman, and M. Mastin, Knot Probabilities in Random Diagrams, arXiv preprint arXiv:1512.05749 [math.GT], 2015. See Tables 1.
• Richard Kapolnai, Gabor Domokos, and Timea Szabo, Generating spherical multiquadrangulations by restricted vertex splittings and the reducibility of equilibrium classes, Periodica Polytechnica Electrical Engineering, 56(1):11-10, 2012. Also arXiv:1206.1698, 2012.

Crossrefs

A054935 is the same but not allowing mirror image as an isomorphism.

Extensions

a(11)-a(18) from Heidi Van den Camp and Brendan McKay, Mar 10 2023