%I A000103 M1423 N0559
%S A000103 0,0,1,1,2,5,12,34,130,525,2472,12400,65619,357504,1992985,11284042,
%T A000103 64719885,375126827,2194439398,12941995397,76890024027,459873914230,
%U A000103 2767364341936,16747182732792
%N A000103 Number of n-node triangulations of sphere in which every node has gdegree 
               >= 4.
%D A000103 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000103 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000103 R. Bowen and S. Fisk, Generation of triangulations of the sphere, Math. 
               Comp., 21 (1967), 250-252.
%D A000103 D. A. Holton and B. D. McKay, The smallest non-hamiltonian 3-connected 
               cubic planar graphs have 38 vertices, J. Combinat. Theory, B 45 (1988), 
               305-319.
%H A000103 Gunnar Brinkmann and Brendan McKay, <a href="http://cs.anu.edu.au/people/
               bdm/plantri/">plantri and fullgen</a> programs for generation of 
               certain types of planar graph.
%H A000103 Thom Sulanke, <a href="http://hep.physics.indiana.edu/~tsulanke/graphs/
               surftri/">Generating triangulations of surfaces (surftri)</a>, (also 
               subpages).
%H A000103 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 17 2009]
%e A000103 a(4)=0, a(5)=0 because the tetrahedron and the 5-bipyramid both have 
               vertices of degree 3. a(6)=1 because of the A000109(6)=2 triangulations 
               with 6 nodes (abcdef) the one corresponding to the octahedron (bcde,
               afec,abfd,acfe,adfb,bedc) has no node of degree 3, whereas the other 
               triangulation (bcdef,afec,abed,ace,adcbf,aeb) has 2 such nodes.
%Y A000103 Cf. all triangulations: A000109, triangulations with minimum degree 5: 
               A081621.
%Y A000103 Sequence in context: A151408 A121956 A131467 this_sequence A101292 A131267 
               A148286
%Y A000103 Adjacent sequences: A000100 A000101 A000102 this_sequence A000104 A000105 
               A000106
%K A000103 nonn,hard
%O A000103 4,5
%A A000103 N. J. A. Sloane (njas(AT)research.att.com).
%E A000103 More terms from Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 24 2003
%E A000103 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm) from the Surftri 
               web site, May 05 2007