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 A126149 Number of connected nonhamiltonian graphs with n nodes. 1
 0, 1, 1, 3, 13, 64, 470, 4921, 83997, 2411453, 123544541, 11537642646, 2013389528672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES J. P. Dolch, Names of Hamiltonian graphs, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 259-271. F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 219. LINKS Jan Goedgebeur, Barbara Meersman, Carol T. Zamfirescu, Graphs with few Hamiltonian Cycles, arXiv:1812.05650 [math.CO], 2018. Eric Weisstein's World of Mathematics, Nonhamiltonian Graph FORMULA a(n) = A001349(n) - A003216(n). EXAMPLE a(10) = A001349(10) - A003216(10) = number of connected graphs on 10 unlabeled nodes - number of Hamiltonian graphs with 10 nodes = 11716571 - 9305118 = 2411453. a(11) = A001349(11) - A003216(11) = number of connected graphs on 11 unlabeled nodes - number of Hamiltonian graphs with 11 nodes = 1006700565 - 883156024 = 123544541. CROSSREFS Cf. A000088, A001349, A003216, A022564. Cf. A246446 (number of not-necessarily-connected simple nonhamiltonian graphs on n nodes). Sequence in context: A065065 A020086 A151987 * A060927 A074537 A284714 Adjacent sequences:  A126146 A126147 A126148 * A126150 A126151 A126152 KEYWORD nonn,more AUTHOR Jonathan Vos Post, Mar 07 2007 EXTENSIONS Terms a(1)-a(9) corrected by Travis Hoppe, Jun 01 2014 a(11) added by Eric W. Weisstein, Aug 26 2014 a(12) from formula by Falk Hüffner, Aug 13 2017 a(13) added by Jan Goedgebeur, May 07 2019 STATUS approved

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Last modified March 31 03:48 EDT 2020. Contains 333136 sequences. (Running on oeis4.)