A002841 Number of 3-connected self-dual planar graphs with 2n edges. (Formerly M1615 N0631)

1, 1, 2, 6, 16, 50, 165, 554, 1908, 6667, 23556, 84048, 302404, 1095536, 3993623

Offset

3,3

Comments

Also number of self-dual polyhedra with n+1 vertices (and n+1 faces). - Franklin T. Adams-Watters, Dec 18 2006

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).

Links

Table of n, a(n) for n=3..17.

Stuart E Anderson, Python program to generate the sequence to a(13), and also generate and separate the self-dual graphs and graph/dual pairs.

C. J. Bouwkamp and N. J. A. Sloane, Correspondence, 1971

M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties, Journal of Combinatorial Theory, Series B, Volume 66, Issue 1, January 1996, Pages 87-122. See bottom of Table IV on page 98.

P. J. Federico, Enumeration of polyhedra: the number of 9-hedra, J. Combin. Theory, 7 (1969), 155-161.

House of Graphs, Planar graphs.

C. A. B. Smith and W. T. Tutte, A class of self-dual maps, Canadian Journal of Mathematics, Volume 2, 1950, pp. 179 - 196.

Eric Weisstein's World of Mathematics, Self-Dual Graph.

Prog

(Python) # See Anderson link

Crossrefs

Cf. A000944.

Sequence in context: A000136 A369365 A013989 * A136509 A100664 A317094

Adjacent sequences: A002838 A002839 A002840 * A002842 A002843 A002844

Keyword

nonn,nice,more

Author

N. J. A. Sloane

Extensions

Definition corrected by Gordon Royle, Dec 15 2005

a(14)-a(17) added by Jan Goedgebeur, Sep 16 2021

Status

approved