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A002880 Number of 3-connected nets with n edges.
(Formerly M0381 N0143)
7
1, 0, 1, 1, 2, 2, 9, 11, 37, 79, 249, 671, 2182, 6692, 22131, 72405, 243806, 822788, 2815119, 9679205, 33551192, 116900081, 409675567, 1442454215, 5102542680, 18124571838, 64634480340, 231334873091, 830828150081, 2993489821771 (list; graph; refs; listen; history; text; internal format)
OFFSET
6,5
COMMENTS
Also, the number of 3-connected quadrangulations without separating 4-cycles (up to orientation) with n faces. - Andrey Zabolotskiy, Sep 20 2019
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
C. J. Bouwkamp & N. J. A. Sloane, Correspondence, 1971
J. A. D. Cameron, Searching for Squared Squares, USYD Master of Science Thesis (1976). Rare Books & Special Collections Fisher Library, Sydney University.
J. A. D. Cameron, Table 7.2 - listing of tri-connected planar graphs by edge, from the thesis - this was the first count of order 20 (22131). Photo by Stuart E Anderson.
G. Brinkmann, S. Greenberg, C. Greenhill, B. D. McKay, R. Thomas, and P. Wollan, Generation of simple quadrangulations of the sphere, Discr. Math., 305 (2005), 33-54.
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
M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties, Journal of Combinatorial Theory Series B 66:1 (1996), 87-122.
P. J. Federico, Enumeration of polyhedra: the number of 9-hedra, J. Combin. Theory, 7 (1969), 155-161.
N. D. Kazarinoff and R. Weitzenkamp, Squaring rectangles and squares, Amer. Math. Monthly, 80 (1973), 877-888.
EXAMPLE
G.f. = x^6 + x^8 + x^9 + 2*x^10 + 2*x^11 + 9*x^12 + 11*x^13 + 37*x^14 + ...
CROSSREFS
Sequence in context: A193726 A143022 A154100 * A225465 A248665 A066324
KEYWORD
nonn,nice
AUTHOR
STATUS
approved

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Last modified April 23 06:04 EDT 2024. Contains 371906 sequences. (Running on oeis4.)