%I A000109 M1469 N0580
%S A000109 1,1,1,2,5,14,50,233,1249,7595,49566,339722,2406841,17490241,
%T A000109 129664753,977526957,7475907149,57896349553,453382272049,
%U A000109 3585853662949,28615703421545
%N 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.
%D A000109 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000109 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000109 J. Bokowski and P. Schuchert, Equifacetted 3-spheres as topes of nonpolytopal 
               matroid polytopes. Discrete Comput. Geom. 13 (1995), no. 3-4, 347-361.
%D A000109 R. Bowen and S. Fisk, Generation of triangulations of the sphere, Math. 
               Comp., 21 (1967), 250-252.
%D A000109 G. Brinkmann and B. McKay, in preparation.
%D A000109 M. Deza, M. Dutour and P. W. Fowler, Zigzags, railroads and knots in 
               fullerenes, J. Chem. Inf. Comput. Sci., 44 (2004), 1282-1293.
%D A000109 M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. 
               Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 
               1992.
%D A000109 P. J. Federico, Enumeration of polyhedra: the number of 9-hedra, J. Combin. 
               Theory, 7 (1969), 155-161.
%D A000109 B. Gr\"{u}nbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.
%D A000109 J. Lederberg, Hamilton circuits of convex trivalent polyhedra (up to 
               18 vertices), Am. Math. Monthly, 74 (1967), 522-527.
%D A000109 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.
%H A000109 David Wasserman, <a href="b000109.txt">Table of n, a(n) for n = 3..23</
               a>
%H A000109 F. H. Lutz, <a href="http://arXiv.org/abs/math.CO/0506372">Triangulated 
               manifolds with few vertices: Combinatorial Manifolds</a>
%H A000109 B. D. McKay, <a href="http://cs.anu.edu.au/~bdm/plantri">Plantri</a>
%H A000109 G. P. Michon, <a href="http://www.numericana.com/data/polyhedra.htm">
               Counting Polyhedra</a>
%H A000109 Thom Sulanke, <a href="http://hep.physics.indiana.edu/~tsulanke/graphs/
               surftri/">Generating triangulations of surfaces (surftri)</a>, (also 
               subpages).
%H A000109 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SimplePolyhedron.html">Link to a section of The World of Mathematics.</
               a>
%H A000109 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%H A000109 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MaximalPlanarGraph.html">Maximal Planar Graph</a> [From Eric W. Weisstein 
               (eric(AT)weisstein.com), Mar 30 2009]
%H A000109 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CubicPolyhedralGraph.html">Cubic Polyhedral Graph</a> [From Eric 
               W. Weisstein (eric(AT)weisstein.com), May 18 2009]
%Y A000109 Cf. A005964, A058378.
%Y A000109 Sequence in context: A100597 A022562 A115340 this_sequence A049338 A115275 
               A000679
%Y A000109 Adjacent sequences: A000106 A000107 A000108 this_sequence A000110 A000111 
               A000112
%K A000109 nonn,nice,hard,core
%O A000109 3,4
%A A000109 N. J. A. Sloane (njas(AT)research.att.com).
%E A000109 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