A007030 Non-Hamiltonian simplicial polyhedra with n nodes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 30, 239, 2369, 22039, 205663, 1879665, 16999932, 152227187, 1353996482

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

Comments

a(18) = 1879665 was conjectured by Dillencourt and verified by direct computation by Sean A. Irvine, Sep 26 2017.

By Steinitz's theorem non-Hamiltonian simplicial polyhedra correspond to non-Hamiltonian maximal planar graphs. - William P. Orrick, Feb 25 2021

Examples

			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
		

References

• M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties, Journal of Combinatorial Theory, Series B, Volume 66, Issue 1, January 1996, Pages 87-122.
• Eric Weisstein's World of Mathematics, Polyhedral Graph
• Wikimedia, Goldner-Harary graphs, additional images of the graph and related simplicial polyhedron created by David Eppstein and Richard J. Mathar. - _William P. Orrick_, Feb 25 2021
• Wikipedia, Goldner-Harary graph

Crossrefs

Cf. A000109, A115340.

Formula

a(n) = A000109(n) - A115340(n-2). - William P. Orrick, Feb 20 2021

Extensions

a(18) from Sean A. Irvine, Sep 26 2017

a(19)-a(21) using new formula by William P. Orrick, Feb 20 2021