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Search: id:A000103
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| A000103 |
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Number of n-node triangulations of sphere in which every node has gdegree >= 4.
(Formerly M1423 N0559)
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+0
3
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| 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; listen)
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OFFSET
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4,5
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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LINKS
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Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Thom Sulanke, Generating triangulations of surfaces (surftri), (also subpages).
Eric Weisstein's World of Mathematics, Cubic Polyhedral Graph [From Eric W. Weisstein (eric(AT)weisstein.com), May 17 2009]
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EXAMPLE
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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.
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CROSSREFS
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Cf. all triangulations: A000109, triangulations with minimum degree 5: A081621.
Adjacent sequences: A000100 A000101 A000102 this_sequence A000104 A000105 A000106
Sequence in context: A151408 A121956 A131467 this_sequence A101292 A131267 A148286
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KEYWORD
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nonn,hard
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 24 2003
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm) from the Surftri web site, May 05 2007
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