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A000109 Number of simplicial polyhedra with n nodes; simple planar graphs with 3n-6 edges; maximal simple planar graphs; 3-connected planar triangulations; 3-connected triangulations of the sphere; 3-connected cubic planar graphs.
(Formerly M1469 N0580)
+0
13
1, 1, 1, 2, 5, 14, 50, 233, 1249, 7595, 49566, 339722, 2406841, 17490241, 129664753, 977526957, 7475907149, 57896349553, 453382272049, 3585853662949, 28615703421545 (list; graph; listen)
OFFSET

3,4

REFERENCES

J. Bokowski and P. Schuchert, Equifacetted 3-spheres as topes of nonpolytopal matroid polytopes. Discrete Comput. Geom. 13 (1995), no. 3-4, 347-361.

R. Bowen and S. Fisk, Generation of triangulations of the sphere, Math. Comp., 21 (1967), 250-252.

G. Brinkmann and B. McKay, in preparation.

M. Deza, M. Dutour and P. W. Fowler, Zigzags, railroads and knots in fullerenes, J. Chem. Inf. Comput. Sci., 44 (2004), 1282-1293.

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

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

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

J. Lederberg, Hamilton circuits of convex trivalent polyhedra (up to 18 vertices), Am. Math. Monthly, 74 (1967), 522-527.

Sciriha, I. and Fowler, P.W., Nonbonding Orbitals in Fullerenes: Nuts and Cores in Singular Polyhedral Graphs J. Chem. Inf. Model., 47, 5, 1763 - 1775, 2007.

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

David Wasserman, Table of n, a(n) for n = 3..23

F. H. Lutz, Triangulated manifolds with few vertices: Combinatorial Manifolds

B. D. McKay, Plantri

G. P. Michon, Counting Polyhedra

Thom Sulanke, Generating triangulations of surfaces (surftri), (also subpages).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for "core" sequences

Eric Weisstein's World of Mathematics, Maximal Planar Graph [From Eric W. Weisstein (eric(AT)weisstein.com), Mar 30 2009]

Eric Weisstein's World of Mathematics, Cubic Polyhedral Graph [From Eric W. Weisstein (eric(AT)weisstein.com), May 18 2009]

CROSSREFS

Cf. A005964, A058378.

Sequence in context: A100597 A022562 A115340 this_sequence A049338 A115275 A000679

Adjacent sequences: A000106 A000107 A000108 this_sequence A000110 A000111 A000112

KEYWORD

nonn,nice,hard,core

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

Extended by Brendan McKay (bdm(AT)cs.anu.edu.au) and Gunnar Brinkmann (Gunnar.Brinkmann(AT)ugent.be) using their program "plantri", Dec 19, 2000

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Last modified December 18 21:37 EST 2009. Contains 171024 sequences.


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