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%I #50 Sep 10 2019 02:54:14
%S 1,2,5,17,80,474,3841,39635,495991,7170657,116171803,2070451150,
%T 40130198979,839266928707,18826133329753
%N Number of cubic Hamiltonian graphs with 2n nodes.
%D McKay, Brendan D.; Royle, Gordon F.; Constructing the cubic graphs on up to 20 vertices. Thirteenth Australasian conference on combinatorial mathematics and computing (Sydney, 1985). Ars Combin. 21 (1986), A, 129-140.
%H F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, <a href="http://alexandria.tue.nl/repository/books/252909.pdf">Computer investigations of cubic graphs</a>, T.H.-Report 76-WSK-01, Technological University Eindhoven, Dept. Mathematics, 1976. [From _N. J. A. Sloane_, Jan 12 2012].
%H Jan Goedgebeur, Barbara Meersman, Carol T. Zamfirescu, <a href="https://arxiv.org/abs/1812.05650">Graphs with few Hamiltonian Cycles</a>, arXiv:1812.05650 [math.CO], 2018.
%H R. J. Mathar, <a href="http://arxiv.org/abs/1109.2358">The Wigner 3n-j Graphs up to 12 Vertices</a>, arXiv preprint arXiv:1109.2358 [math-ph], 2011-2012.
%H Roman Maurer, <a href="http://www.ijp.si/vega/HtmlDoc/MANUAL/HAMCUB2.HTM">Counting small hamiltonian cubic graphs</a>.
%H Roman Maurer, <a href="http://vega.ijp.si/doku.php">vega06.zip</a> [substitute for the broken link above] [From _R. J. Mathar_, Sep 22 2010]
%H R. W. Pratt, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.9058">The complete catalog of 3-regular diameter-3 planar graphs</a>, Table 2 (1996)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicGraph.html">Cubic Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianGraph.html">Hamiltonian Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LCFNotation.html">LCF Notation</a>
%F a(n) = A002851(n) - A164919(n). - _R. J. Mathar_, Sep 22 2010
%K nonn,hard,nice,more
%O 2,2
%A Martin Harborth (Martin.Harborth(AT)vt.siemens.de)
%E a(11) from _Vladeta Jovovic_, Jul 02 2007
%E a(12) from _Sean A. Irvine_, Sep 25 2015
%E a(13) from _Sean A. Irvine_, Oct 06 2015
%E a(14)-a(16) from _Jan Goedgebeur_, Sep 07 2019
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