A002840 Number of polyhedral graphs with n edges.

1, 0, 1, 2, 2, 4, 12, 22, 58, 158, 448, 1342, 4199, 13384, 43708, 144810, 485704, 1645576, 5623571, 19358410, 67078828, 233800162, 819267086, 2884908430, 10204782956, 36249143676, 129267865144, 462669746182, 1661652306539, 5986979643542

Offset: 6

Author

N. J. A. Sloane

Keywords

• nonn
• nice

References

• M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• T. R. S. Walsh, personal communication.

Links

• C. J. Bouwkamp & N. J. A. Sloane, Correspondence, 1971
• A. J. W. Duijvestijn and P. J. Federico, The number of polyhedral (3-connected planar) graphs, Math. Comp. 37 (1981), no. 156, 523-532.
• P. J. Federico, Enumeration of polyhedra: the number of 9-hedra, J. Combin. Theory, 7 (1969), 155-161.
• G. P. Michon, Counting Polyhedra - Numericana
• Hugo Pfoertner, Unlabeled 3-connected planar graphs for n<=20 edges, list in PARI-readable format.
• Eric Weisstein's World of Mathematics, Polyhedral Graph
• T. R. S. Walsh, Number of sensed planar maps with n edges and m vertices

Crossrefs

Column sums of A049337.

Cf. A002841, A000944, A046091, A338511, A343869, A343871.

Programs

PARI

\\ It is assumed that the 3cp.gp file (from the linked zip archive) has been read before, i.e., \r [path]3cp.gp
for(k=6,#ThreeConnectedData,print1(#ThreeConnectedData[k],", "));
\\ printing of the edge lists of the graphs for n <= 11
print(ThreeConnectedData[6..11]) \\ Hugo Pfoertner, Feb 14 2021

Extensions

a(30)-a(35) from the Numericana link added by Andrey Zabolotskiy, Jun 13 2020