cp's OEIS Frontend

A000944 Number of polyhedra (or 3-connected simple planar graphs) with n nodes.

%I A000944 M1796 N0709 #61 Sep 01 2025 11:33:38
%S A000944 0,0,0,1,2,7,34,257,2606,32300,440564,6384634,96262938,1496225352,
%T A000944 23833988129,387591510244,6415851530241,107854282197058
%N A000944 Number of polyhedra (or 3-connected simple planar graphs) with n nodes.
%D A000944 H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, B15.
%D A000944 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 A000944 B. Grünbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.
%D A000944 Y. Y. Prokhorov, ed., Mnogogrannik [Polyhedron], Mathematical Encyclopedia Dictionary, Soviet Encyclopedia, 1988.
%D A000944 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000944 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A000944 G. M. Ziegler, Questions about polytopes, pp. 1195-1211 of Mathematics Unlimited - 2001 and Beyond, ed. B. Engquist and W. Schmid, Springer-Verlag, 2001.
%H A000944 Gunnar Brinkmann and Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/plantri/">plantri and fullgen</a> programs for generation of certain types of planar graph.
%H A000944 Gunnar Brinkmann and Brendan McKay, <a href="/A000103/a000103_1.pdf">plantri and fullgen</a> programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
%H A000944 CombOS - Combinatorial Object Server, <a href="http://combos.org/plantri">generate planar graphs</a>
%H A000944 A. J. W. Duijvestijn and P. J. Federico, <a href="https://doi.org/10.1090/S0025-5718-1981-0628713-3">The number of polyhedral (3-connected planar) graphs</a>, Math. Comp. 37 (1981), no. 156, 523-532. MR0243424 (39 #4746).
%H A000944 P. J. Federico, <a href="http://dx.doi.org/10.1016/S0021-9800(69)80050-5">Enumeration of polyhedra: the number of 9-hedra</a>, J. Combin. Theory, 7 (1969), 155-161.
%H A000944 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018.
%H A000944 Lukas Finschi, <a href="http://dx.doi.org/10.3929/ethz-a-004255224">A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids</a>, A dissertation submitted to the Swiss Federal Institute of Technology, Zurich for the degree of Doctor of Mathematics, 2001. See p. 155.
%H A000944 Moritz Firsching,  <a href="https://doi.org/10.1007/s10107-017-1120-0">Realizability and inscribability for simplicial polytopes via nonlinear optimization</a>.  Math. Program. 166, No. 1-2 (A), 273-295 (2017). Table 1
%H A000944 Komei Fukuda, Hiroyuki Miyata, and Sonoko Moriyama, <a href="http://arxiv.org/abs/1204.0645">Complete Enumeration of Small Realizable Oriented Matroids</a>, arXiv:1204.0645 [math.CO], 2012; Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. - From _N. J. A. Sloane_, Feb 16 2013
%H A000944 Jorik Jooken, <a href="https://www.arxiv.org/abs/2508.20825">Computer-assisted graph theory: a survey</a>, arXiv:2508.20825 [math.CO], 2025. See Ref. 196 at p. 5.
%H A000944 A. B. Korchagin, <a href="http://dx.doi.org/10.1007/s00454-007-9008-z">Ordering Cellular Spaces with Application to Curves and Knots</a>, Discrete Comput. Geom., 40 (2008), 289-311.
%H A000944 G. P. Michon, <a href="http://www.numericana.com/data/polyhedra.htm">Counting Polyhedra</a>
%H A000944 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolyhedralGraph.html">Polyhedral Graph</a>
%Y A000944 Cf. A005470, A049337, A049334, A003094, A049336, A021103, A005841.
%Y A000944 Row sums of A212438.
%K A000944 nonn,nice,hard,more,changed
%O A000944 1,5
%A A000944 _N. J. A. Sloane_
%E A000944 More terms from _Brendan McKay_
%E A000944 a(18) from _Brendan McKay_, Jun 02 2006