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

1,2

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

Links

Table of n, a(n) for n=1..18.

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.

Example

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.

Crossrefs

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

Sequence in context: A369083 A201794 A188229 * A098644 A182322 A132105

Adjacent sequences: A277736 A277737 A277738 * A277740 A277741 A277742

Keyword

nonn,more

Author

N. J. A. Sloane, Nov 07 2016

Extensions

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

Status

approved