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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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

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 4 23:11 EST 2009. Contains 170347 sequences.


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