A000944 Number of polyhedra (or 3-connected simple planar graphs) with n nodes. (Formerly M1796 N0709)

0, 0, 0, 1, 2, 7, 34, 257, 2606, 32300, 440564, 6384634, 96262938, 1496225352, 23833988129, 387591510244, 6415851530241, 107854282197058

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.

B. Grünbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.

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.

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

A. J. W. Duijvestijn and P. J. Federico, The number of polyhedral (3-connected planar) graphs, Math. Comp. 37 (1981), no. 156, 523-532. MR0243424 (39 #4746).

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

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018.

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.

Firsching, Moritz Realizability and inscribability for simplicial polytopes via nonlinear optimization. Math. Program. 166, No. 1-2 (A), 273-295 (2017). Table 1

Fukuda, Komei; Miyata, Hiroyuki; Moriyama, Sonoko. Complete Enumeration of Small Realizable Oriented Matroids. Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. Also arXiv:1204.0645. - From N. J. A. Sloane, Feb 16 2013

A. B. Korchagin, Ordering Cellular Spaces with Application to Curves and Knots, Discrete Comput. Geom., 40 (2008), 289-311.

G. P. Michon, Counting Polyhedra

Eric Weisstein's World of Mathematics, Polyhedral Graph

Crossrefs

Cf. A005470, A049337, A049334, A003094, A049336, A021103, A005841.

Row sums of A212438.

Sequence in context: A294466 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