cp's OEIS Frontend

A007030 Non-Hamiltonian simplicial polyhedra with n nodes.

%I A007030 M2152 #40 Jul 08 2025 16:58:55
%S A007030 0,0,0,0,0,0,0,0,0,0,1,2,30,239,2369,22039,205663,1879665,16999932,
%T A007030 152227187,1353996482
%N A007030 Non-Hamiltonian simplicial polyhedra with n nodes.
%C A007030 a(18) = 1879665 was conjectured by Dillencourt and verified by direct computation by _Sean A. Irvine_, Sep 26 2017.
%C A007030 By Steinitz's theorem non-Hamiltonian simplicial polyhedra correspond to non-Hamiltonian maximal planar graphs. - _William P. Orrick_, Feb 25 2021
%D A007030 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 A007030 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007030 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 A007030 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolyhedralGraph.html">Polyhedral Graph</a>
%H A007030 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 A007030 Wikipedia, <a href="https://en.wikipedia.org/wiki/Goldner%E2%80%93Harary_graph">Goldner-Harary graph</a>
%F A007030 a(n) = A000109(n) - A115340(n-2). - _William P. Orrick_, Feb 20 2021
%e A007030 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 A007030 Cf. A000109, A115340.
%K A007030 nonn,hard,more
%O A007030 1,12
%A A007030 _N. J. A. Sloane_
%E A007030 a(18) from _Sean A. Irvine_, Sep 26 2017
%E A007030 a(19)-a(21) using new formula by _William P. Orrick_, Feb 20 2021