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%I M2152 #35 Feb 25 2021 13:26:12
%S 0,0,0,0,0,0,0,0,0,0,1,2,30,239,2369,22039,205663,1879665,16999932,
%T 152227187,1353996482
%N Non-Hamiltonian simplicial polyhedra with n nodes.
%C a(18) = 1879665 was conjectured by Dillencourt and verified by direct computation by _Sean A. Irvine_, Sep 26 2017.
%C By Steinitz's theorem non-Hamiltonian simplicial polyhedra correspond to non-Hamiltonian maximal planar graphs. - _William P. Orrick_, Feb 25 2021
%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 and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H M. B. Dillencourt, <a href="http://dx.doi.org/10.1006/jctb.1996.0008">Polyhedra of small orders and their Hamiltonian properties</a>, Journal of Combinatorial Theory, Series B, Volume 66, Issue 1, January 1996, Pages 87-122.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolyhedralGraph.html">Polyhedral Graph</a>
%H Wikimedia, <a href="https://commons.wikimedia.org/wiki/Category:Goldner%E2%80%93Harary_graphs">Goldner-Harary graphs</a>, additional images of the graph and related simplicial polyhedron created by David Eppstein and Richard J. Mathar. - _William P. Orrick_, Feb 25 2021
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Goldner%E2%80%93Harary_graph">Goldner-Harary graph</a>
%F a(n) = A000109(n) - A115340(n-2). - _William P. Orrick_, Feb 20 2021
%e The unique non-Hamiltonian maximal planar graph of 11 vertices is the Goldner-Harary graph. A corresponding simplicial polyhedron can be obtained by attaching a tetrahedron to each of the six faces of a triangular bipyramid. - _William P. Orrick_, Feb 25 2021
%Y Cf. A000109, A115340.
%K nonn,hard,more
%O 1,12
%A _N. J. A. Sloane_.
%E a(18) from _Sean A. Irvine_, Sep 26 2017
%E a(19)-a(21) using new formula by _William P. Orrick_, Feb 20 2021
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