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A007022 Number of 4-regular polyhedra with n nodes.
(Formerly M2290)
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 (list; graph; refs; listen; history; text; internal format)



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


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


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), 33-54. 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]

M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties, Journal of Combinatorial Theory Series B 66:1 (1996), 87-122.

S. V. Jablan, L. M. Radović, and R. Sazdanović, Basic polyhedra in knot theory Kragujevac J. Math., 28 (2005), 155-164.


Cf. A000944 (all polyhedral graphs), A113204, A078672, A078666 (total number of simple 4-regular 4-edge-connected planar maps, including not 3-connected ones).

Sequence in context: A281905 A278835 A163932 * A011950 A289883 A280564

Adjacent sequences:  A007019 A007020 A007021 * A007023 A007024 A007025




N. J. A. Sloane, Apr 28 1994


More terms from Hugo Pfoertner, Mar 22 2003

a(31) corrected by Brendan McKay, Jun 22 2006

a(1)=a(2)=...=a(7)=0 prepended by Max Alekseyev, Sep 12 2016

Two leading zeroes removed to match the definition by Andrey Zabolotskiy, Aug 22 2017



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Last modified October 22 18:55 EDT 2018. Contains 316500 sequences. (Running on oeis4.)