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A002840 Number of polyhedral graphs with n edges.
(Formerly M0339 N0129)
17

%I M0339 N0129 #44 May 06 2021 22:14:13

%S 1,0,1,2,2,4,12,22,58,158,448,1342,4199,13384,43708,144810,485704,

%T 1645576,5623571,19358410,67078828,233800162,819267086,2884908430,

%U 10204782956,36249143676,129267865144,462669746182,1661652306539,5986979643542

%N Number of polyhedral graphs with n edges.

%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 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%D T. R. S. Walsh, personal communication.

%H C. J. Bouwkamp & N. J. A. Sloane, <a href="/A000162/a000162.pdf">Correspondence, 1971</a>

%H 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.

%H 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 G. P. Michon, <a href="http://www.numericana.com/data/polyhedra.htm">Counting Polyhedra - Numericana</a>

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a002840_3cp.zip">Unlabeled 3-connected planar graphs for n<=20 edges</a>, list in PARI-readable format.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolyhedralGraph.html">Polyhedral Graph</a>

%H T. R. S. Walsh, <a href="/A007401/a007401.pdf">Number of sensed planar maps with n edges and m vertices</a>

%o (PARI) \\ It is assumed that the 3cp.gp file (from the linked zip archive) has been read before, i.e., \r [path]3cp.gp

%o for(k=6,#ThreeConnectedData,print1(#ThreeConnectedData[k],", "));

%o \\ printing of the edge lists of the graphs for n <= 11

%o print(ThreeConnectedData[6..11]) \\ _Hugo Pfoertner_, Feb 14 2021

%Y Column sums of A049337.

%Y Cf. A002841, A000944, A046091, A338511, A343869, A343871.

%K nonn,nice

%O 6,4

%A _N. J. A. Sloane_

%E a(30)-a(35) from the Numericana link added by _Andrey Zabolotskiy_, Jun 13 2020

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)