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A000944 Number of polyhedra (or 3-connected simple planar graphs) with n nodes.
(Formerly M1796 N0709)
15
0, 0, 0, 1, 2, 7, 34, 257, 2606, 32300, 440564, 6384634, 96262938, 1496225352, 23833988129, 387591510244, 6415851530241, 107854282197058 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

REFERENCES

H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, B15.

M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.

Duijvestijn, A. J. W.; Federico, P. J.; The number of polyhedral (3-connected planar) graphs. Math. Comp. 37 (1981), no. 156, 523-532.

Federico, P. J., Enumeration of polyhedra: The number of 9-hedra. J. Combinatorial Theory 7 1969 155--161. MR0243424 (39 #4746)

Lukas Finschi, A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids, A dissertation submitted to the Swiss Federal Institute of Technology, Zurich for the degree of Doctor of Mathematics, 2001. See p. 155.

Fukuda, Komei; Miyata, Hiroyuki; Moriyama, Sonoko. Complete Enumeration of Small Realizable Oriented Matroids. Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. - From N. J. A. Sloane, Feb 16 2013

B. Gr\"{u}nbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.

A. B. Korchagin, Ordering cellular spaces ..., Discrete Comput. Geom., 40 (2008), 289-311.

Y. Y. Prokhorov, ed., Mnogogrannik [Polyhedron], Mathematical Encyclopedia Dictionary, Soviet Encyclopedia, 1988.

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).

G. M. Ziegler, Questions about polytopes, pp. 1195-1211 of Mathematics Unlimited - 2001 and Beyond, ed. B. Engquist and W. Schmid, Springer-Verlag, 2001.

LINKS

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

G. Brinkmannm and B. McKay, Program for generating these objects..

G. P. Michon, Counting Polyhedra

Eric Weisstein's World of Mathematics, Polyhedral Graph

CROSSREFS

Cf. A005470, A049337, A049334, A003094, A049336, A021103.

Row sums of A212438.

Sequence in context: A049463 A029894 A110313 * A136310 A222868 A222777

Adjacent sequences:  A000941 A000942 A000943 * A000945 A000946 A000947

KEYWORD

nonn,nice,hard,more

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Brendan McKay.

a(18) from Brendan McKay, Jun 02 2006

STATUS

approved

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Last modified October 24 16:46 EDT 2014. Contains 248516 sequences.