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A078666
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Number of isomorphism classes of simple quadrangulations of the sphere having n vertices and n-2 faces, minimal degree 3, with orientation-reversing isomorphisms permitted.
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7
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1, 0, 1, 1, 3, 3, 12, 19, 64, 155, 510, 1514, 5146, 16966, 58782, 203269, 716607, 2536201, 9062402, 32533568, 117498072, 426212952, 1553048548, 5681011890, 20858998805, 76850220654, 284057538480, 1053134292253, 3915683667721
(list; graph; refs; listen; history; internal format)
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OFFSET
| 8,5
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COMMENTS
| Number of basic polyhedra with n vertices.
Initial terms of sequence coincide with A007022. Starting from n=12, to it is added the number of simple 4-regular 4-edge-connected but not 3-connected plane graphs on n nodes (A078672). As a result we obtain the number of basic polyhedra.
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REFERENCES
| Gunnar Brinkmann, Sam Greenberg, Catherine Greenhill, Brendan D. McKay, Robin Thomas and Paul Wollan, Generation of simple quadrangulations of the sphere, Discr. Math., 305 (2005), 33-54.
A. Caudron, Classification des noeuds et des enlancements. Public. Math. d'Orsay 82. Orsay: Univ. Paris Sud, Dept. Math., 1982.
J. H. Conway, An enumeration of knots and links and some of their related properties. Computational Problems in Abstract Algebra, Proc. Conf. Oxford 1967 (Ed. J. Leech), 329-358. New York: Pergamon Press, 1970.
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LINKS
| G. Brinkmann et al., Generation of simple quadrangulations of the sphere
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
S. V. Jablan, Ordering Knots
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EXAMPLE
| a(6)=1, a(7)=0, a(8)=1, a(9)=1, a(10)=3, etc.
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CROSSREFS
| Cf. A007022, A078672, A113201.
Sequence in context: A073055 A074850 A075780 * A006804 A052533 A136533
Adjacent sequences: A078663 A078664 A078665 * A078667 A078668 A078669
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KEYWORD
| nonn
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AUTHOR
| Slavik V. Jablan (jablans(AT)yahoo.com) and Brendan McKay (bdm(AT)cs.anu.edu.au) Feb 06 2003
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