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A000103 Number of n-node triangulations of sphere in which every node has degree >= 4.
(Formerly M1423 N0559)
26
0, 0, 1, 1, 2, 5, 12, 34, 130, 525, 2472, 12400, 65619, 357504, 1992985, 11284042, 64719885, 375126827, 2194439398, 12941995397, 76890024027, 459873914230, 2767364341936, 16747182732792 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,5

REFERENCES

R. Bowen and S. Fisk, Generation of triangulations of the sphere, Math. Comp., 21 (1967), 250-252.

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.

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

Table of n, a(n) for n=4..27.

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]

Thom Sulanke, Generating triangulations of surfaces (surftri), (also subpages).

Eric Weisstein's World of Mathematics, Cubic Polyhedral Graph

EXAMPLE

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.

CROSSREFS

Cf. all triangulations: A000109, triangulations with minimum degree 5: A081621.

Sequence in context: A121956 A176638 A131467 * A101292 A181899 A131267

Adjacent sequences:  A000100 A000101 A000102 * A000104 A000105 A000106

KEYWORD

nonn,hard,more

AUTHOR

N. J. A. Sloane

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

STATUS

approved

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Last modified May 26 12:21 EDT 2017. Contains 287095 sequences.