A000103 Number of n-node triangulations of sphere in which every node has degree >= 4.
0, 0, 1, 1, 2, 5, 12, 34, 130, 525, 2472, 12400, 65619, 357504, 1992985, 11284042, 64719885, 375126827, 2194439398, 12941995397, 76890024027, 459873914230, 2767364341936, 16747182732792
Offset: 4
Examples
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.
References
- 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
- R. Bowen and S. Fisk, Generation of triangulations of the sphere, Math. Comp., 21 (1967), 250-252.
- R. Bowen and S. Fisk, Generation of triangulations of the sphere [Annotated scanned copy]
- Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
- Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
- CombOS - Combinatorial Object Server, generate planar graphs
- R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
- D. A. Holton and B. D. McKay, The smallest non-hamiltonian 3-connected cubic planar graphs have 38 vertices, J. Combinat. Theory B vol 45, iss. 3 (1988) 305-319.
- D. A. Holton and B. D. McKay, Erratum, J. Combinat. Theory B vol 47, iss. 2 (1989) 248.
- J. Lederberg, Dendral-64, II, Report to NASA, Dec 1965 [Annotated scanned copy]
- Thom Sulanke, Generating triangulations of surfaces (surftri), (also subpages).
- Eric Weisstein's World of Mathematics, Cubic Polyhedral Graph
Extensions
More terms from Hugo Pfoertner, Mar 24 2003
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm) from the Surftri web site, May 05 2007