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Number of 4-connected simplicial polyhedra with n nodes.
(Formerly M1214)
9

%I M1214 #41 Mar 17 2023 06:52:04

%S 1,1,1,1,1,2,4,10,25,87,313,1357,6244,30926,158428,836749,4504607,

%T 24649284,136610879,765598927,4332047595,24724362117,142205424580,

%U 823687567019,4801749063379

%N Number of 4-connected simplicial polyhedra with n nodes.

%C Also the number of 4-connected triangulations on n vertices. - _Manfred Scheucher_, Mar 17 2023

%D M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.

%D H. Heesch, Ein zum Vierfarbensatz aquivalenter Satz der Panisochromie [ A theorem of panisochromaticity equivalent to the four color theorem ], pp. 229-253 of Graph Theory in Memory of G. A. Dirac (Sandbjerg, 1985). Edited by L. D. Andersen et al., Annals of Discrete Mathematics, 41. North-Holland Publishing Co., Amsterdam-New York, 1989.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Gunnar Brinkmann and Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/plantri/plantri-guide.txt">Guide to using plantri</a>

%H Gunnar Brinkmann and Brendan McKay, <a href="/A007021/a007021.txt">Guide to using plantri</a> [Cached copy, with permission]

%H S. Butler et al., <a href="http://dx.doi.org/10.1007/s00454-009-9216-9">Irreducible Apollonian configurations and packings</a>, Discrete and Computational Geometry, 44 (2010), 487-507.

%H CombOS - Combinatorial Object Server, <a href="http://combos.org/plantri">generate planar graphs</a>

%H Paul Jungeblut, <a href="https://i11www.iti.kit.edu/_media/teaching/theses/ma-jungeblut-19.pdf">Edge Guarding Plane Graphs</a>, Master Thesis, Karlsruhe Institute of Technology (Germany, 2019).

%H Irene Pivotto and Gordon Royle, <a href="https://arxiv.org/abs/1901.10683">Highly-connected planar cubic graphs with few or many Hamilton cycles</a>, arXiv:1901.10683 [math.CO], 2019.

%H Manfred Scheucher, Hendrik Schrezenmaier, and Raphael Steiner, <a href="https://arxiv.org/abs/1811.06482">A Note On Universal Point Sets for Planar Graphs</a>, arXiv:1811.06482 [math.CO], 2018.

%Y Cf. A000109, A007027, A111358.

%K nonn

%O 3,6

%A _N. J. A. Sloane_

%E More terms generated with plantri by _Moritz Firsching_, Aug 20 2015