A113203
Number of isomorphism classes of simple quadrangulations of the sphere having n vertices and n-2 faces, minimal degree 3, with orientation-reversing isomorphisms forbidden.
Original entry on oeis.org
1, 0, 1, 1, 4, 3, 16, 26, 99, 256, 895, 2789, 9740, 32799, 115024, 401180, 1421170, 5046539, 18066772, 64940825, 234712099, 851801048, 3104690139, 11358900851, 41710948878, 153684688127, 568079430741, 2106188450292
Offset: 8
- 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
A308588
Number of 4-regular 3-connected planar graphs with n vertices having an Eulerian tour for which no two consecutive edges are incident with the same face.
Original entry on oeis.org
1, 1, 1, 1, 3, 5, 17, 40, 145, 355, 1264, 3931, 12999, 44727
Offset: 8
- Stuart E Anderson, Illustrations of a(8) to a(14) 4-regular 3-connected planar graphs with n vertices having an Eulerian tour for which no two consecutive edges are incident with the same face.
A007023
Number of 4-connected 4-regular polyhedra with n nodes.
Original entry on oeis.org
1, 0, 1, 0, 3, 1, 8, 7, 37, 55, 220, 499, 1862, 5174, 18258, 57107, 198474
Offset: 6
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- M. B. Dillencourt, Polyhedra of small order and their Hamiltonian properties, Journal of Combinatorial Theory, Series B, Volume 66, Issue 1, January 1996, Pages 87-122. Also Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.
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