

A007030


NonHamiltonian simplicial polyhedra with n nodes.
(Formerly M2152)


3



0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 30, 239, 2369, 22039, 205663, 1879665, 16999932, 152227187, 1353996482
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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 nonHamiltonian simplicial polyhedra correspond to nonHamiltonian maximal planar graphs.  William P. Orrick, Feb 25 2021


REFERENCES

M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 9291, 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

Table of n, a(n) for n=1..21.
M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties, Journal of Combinatorial Theory, Series B, Volume 66, Issue 1, January 1996, Pages 87122.
Eric Weisstein's World of Mathematics, Polyhedral Graph
Wikimedia, GoldnerHarary 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, GoldnerHarary graph


FORMULA

a(n) = A000109(n)  A115340(n2).  William P. Orrick, Feb 20 2021


EXAMPLE

The unique nonHamiltonian maximal planar graph of 11 vertices is the GoldnerHarary 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

Cf. A000109, A115340.
Sequence in context: A089288 A232602 A154413 * A157054 A092355 A215237
Adjacent sequences: A007027 A007028 A007029 * A007031 A007032 A007033


KEYWORD

nonn,hard,more


AUTHOR

N. J. A. Sloane.


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



