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%I M2373 #25 Mar 21 2019 16:48:36
%S 1,0,1,1,3,4,12,23,71,187,627,1970,6833,23384,82625,292164,1045329,
%T 3750277,13532724,48977625,177919099,648145255,2368046117,8674199554,
%U 31854078139,117252592450,432576302286,1599320144703,5925181102878
%N Number of cyclically-5-connected planar trivalent graphs with 2n nodes.
%C This sequence and A111358 are the same sequence. The correspondence is just that these objects are planar duals of each other. But the offset and step are different: if the cubic graph has 2*n vertices, the dual triangulation has n+2 vertices. - _Brendan McKay_, May 24 2017
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H D. A. Holton and B. D. McKay, <a href="http://dx.doi.org/10.1016/0095-8956(88)90075-5">The smallest non-hamiltonian 3-connected cubic planar graphs have 38 vertices</a>, J. Combinat. Theory B vol 45, iss. 3 (1988) 305-319.
%H D. A. Holton and B. D. McKay, <a href="http://dx.doi.org/10.1016/0095-8956(89)90025-7">Erratum</a>, J. Combinat. Theory B vol 47, iss. 2 (1989) 248.
%H B. McKay, <a href="/A006791/a006791.pdf">Email to N. J. A. Sloane, Jul. 1991</a>
%H Irene Pivotto, 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.
%Y Cf. A111358.
%K nonn
%O 10,5
%A _N. J. A. Sloane_.