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%I M1423 N0559 #50 Sep 20 2019 04:45:05
%S 0,0,1,1,2,5,12,34,130,525,2472,12400,65619,357504,1992985,11284042,
%T 64719885,375126827,2194439398,12941995397,76890024027,459873914230,
%U 2767364341936,16747182732792
%N Number of n-node triangulations of sphere in which every node has degree >= 4.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. Bowen and S. Fisk, <a href="http://dx.doi.org/10.1090/S0025-5718-1967-0223277-3">Generation of triangulations of the sphere</a>, Math. Comp., 21 (1967), 250-252.
%H R. Bowen and S. Fisk, <a href="/A000103/a000103.pdf">Generation of triangulations of the sphere</a> [Annotated scanned copy]
%H Gunnar Brinkmann and Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/plantri/">plantri and fullgen</a> programs for generation of certain types of planar graph.
%H Gunnar Brinkmann and Brendan McKay, <a href="/A000103/a000103_1.pdf">plantri and fullgen</a> programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
%H CombOS - Combinatorial Object Server, <a href="http://combos.org/plantri">generate planar graphs</a>
%H R. K. Guy, <a href="/A005347/a005347.pdf">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
%H D. A. Holton and B. D. McKay, <a href="http://dx.doi.org/10.1016/0095-8956(88)90075-5">The smallest non-hamiltonian 3-connected cubic planar graphs have 38 vertices</a>, J. Combinat. Theory B vol 45, iss. 3 (1988) 305-319.
%H D. A. Holton and B. D. McKay, <a href="http://dx.doi.org/10.1016/0095-8956(89)90025-7">Erratum</a>, J. Combinat. Theory B vol 47, iss. 2 (1989) 248.
%H J. Lederberg, <a href="/A000602/a000602_10.pdf">Dendral-64, II</a>, Report to NASA, Dec 1965 [Annotated scanned copy]
%H Thom Sulanke, <a href="http://hep.physics.indiana.edu/~tsulanke/graphs/surftri/">Generating triangulations of surfaces (surftri)</a>, (also subpages).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicPolyhedralGraph.html">Cubic Polyhedral Graph</a>
%e 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 Cf. all triangulations: A000109, triangulations with minimum degree 5: A081621.
%K nonn,hard,more
%O 4,5
%A _N. J. A. Sloane_
%E More terms from _Hugo Pfoertner_, Mar 24 2003
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm) from the Surftri web site, May 05 2007
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