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%I M2764 #55 Jun 30 2023 07:04:48
%S 1,0,1,3,8,48,383,6196,177083,9305118,883156024,152522187830,
%T 48322518340547
%N Number of Hamiltonian graphs with n nodes.
%C a(1) could also be taken to be 0, but I prefer a(1) = 1. - _N. J. A. Sloane_, Oct 15 2006
%D J. P. Dolch, Names of Hamiltonian graphs, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 259-271.
%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 219.
%D R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H John Asplund, N. Bradley Fox, and Arran Hamm, <a href="https://arxiv.org/abs/1804.02473">New Perspectives on Neighborhood-Prime Labelings of Graphs</a>, arXiv:1804.02473 [math.CO], 2018.
%H J. P. Dolch, <a href="/A001349/a001349.pdf">Names of Hamiltonian graphs</a>, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 259-271. (Annotated scanned copy of 3 pages)
%H Scott Garrabrant and Igor Pak, <a href="http://www.math.ucla.edu/~pak/papers/PatternAvoid10.pdf">Pattern Avoidance is Not P-Recursive</a>, preprint, 2015.
%H Scott Garrabrant and Igor Pak, <a href="http://arxiv.org/abs/1505.06508">Pattern Avoidance is Not P-Recursive</a>, arXiv:1505.06508 [math.CO], 2015.
%H Jan Goedgebeur, Barbara Meersman, and Carol T. Zamfirescu, <a href="https://arxiv.org/abs/1812.05650">Graphs with few Hamiltonian Cycles</a>, arXiv:1812.05650 [math.CO], 2018-2019.
%H Peter Steinbach, <a href="/A000088/a000088_17.pdf">Field Guide to Simple Graphs, Volume 1</a>, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianGraph.html">Hamiltonian Graph</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>
%H Gus Wiseman, <a href="/A003216/a003216.png">Non-isomorphic representatives of the a(5) = 8 simple graphs containing a Hamiltonian cycle</a>.
%F A000088(n) = a(n) + A246446(n). - _Gus Wiseman_, Jun 17 2019
%Y Main diagonal of A325455 and of A325447 (for n>=3).
%Y The labeled case is A326208.
%Y The directed case is A326226 (with loops) or A326225 (without loops).
%Y The case without loops is A326215.
%Y Unlabeled simple graphs not containing a Hamiltonian cycle are A246446.
%Y Unlabeled simple graphs containing a Hamiltonian path are A057864.
%Y Cf. A000088, A006125, A283420.
%K nonn,nice,hard,more
%O 1,4
%A _N. J. A. Sloane_
%E Extended to n=11 by _Brendan McKay_, Jul 15 1996
%E a(12) from _Sean A. Irvine_, Mar 17 2015
%E a(13) from A246446 added by _Jan Goedgebeur_, Sep 07 2019
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