

A007022


Number of 4regular polyhedra with n nodes.
(Formerly M2290)


12



0, 0, 0, 0, 0, 1, 0, 1, 1, 3, 3, 11, 18, 58, 139, 451, 1326, 4461, 14554, 49957, 171159, 598102, 2098675, 7437910, 26490072, 94944685, 341867921, 1236864842, 4493270976, 16387852863, 59985464681, 220320405895, 811796327750, 3000183106119
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OFFSET

1,10


COMMENTS

Number of simple 4regular 4edgeconnected 3connected planar graphs; by Steinitz's theorem, every such graph corresponds to a single planar map up to orientationreversing isomorphism. Equivalently, number of 3connected quadrangulations of sphere with orientationreversing isomorphisms permitted with n faces.  Andrey Zabolotskiy, Aug 22 2017


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..34.
G. Brinkmann, S. Greenberg, C. Greenhill, B. D. McKay, R. Thomas, and P. Wollan, Generation of simple quadrangulations of the sphere, Discr. Math., 305 (2005), 3354. doi:10.1016/j.disc.2005.10.005
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
CombOS  Combinatorial Object Server, generate planar graphs
M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties, Journal of Combinatorial Theory Series B 66:1 (1996), 87122.
S. V. Jablan, L. M. Radović, and R. Sazdanović, Basic polyhedra in knot theory, Kragujevac J. Math., 28 (2005), 155164.
T. Tarnai, F. Kovács, P. W. Fowler, and S. D. Guest, Wrapping the cube and other polyhedra, Proc. Roy. Soc. A 468(2145) (2012), 26522666. DOI: 10.1098/rspa.2012.0116.


EXAMPLE

For n=6, the sole 6vertex 4regular polyhedron is the octahedron. The corresponding 6face quadrangulation is its dual graph, i. e., the cube graph.


CROSSREFS

Cf. A000944 (all polyhedral graphs), A113204, A078672, A078666 (total number of simple 4regular 4edgeconnected planar maps, including not 3connected ones).
Sequence in context: A281905 A278835 A163932 * A011950 A289883 A280564
Adjacent sequences: A007019 A007020 A007021 * A007023 A007024 A007025


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 28 1994


EXTENSIONS

More terms from Hugo Pfoertner, Mar 22 2003
a(29) corrected by Brendan McKay, Jun 22 2006
Leading zeros prepended by Max Alekseyev, Sep 12 2016
Offset corrected by Andrey Zabolotskiy, Aug 22 2017


STATUS

approved



