Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #52 Aug 05 2024 13:37:09
%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/pdf/2506025ac933a724edd5cd1be73d344a06b55dad">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