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URL: https://oeis.org/A007030

⇱ A007030 - OEIS

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A007030
Non-Hamiltonian simplicial polyhedra with n nodes.
3
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 30, 239, 2369, 22039, 205663, 1879665, 16999932, 152227187, 1353996482
OFFSET
1,12
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
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
FORMULA
a(n) = A000109(n) - A115340(n-2). - William P. Orrick, Feb 20 2021
EXAMPLE
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
CROSSREFS
Sequence in context: A089288 A232602 A154413 * A157054 A092355 A215237
KEYWORD
nonn,hard,more
EXTENSIONS
a(18) from Sean A. Irvine, Sep 26 2017
a(19)-a(21) using new formula by William P. Orrick, Feb 20 2021
STATUS
approved