cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A126149 Number of connected nonhamiltonian graphs with n nodes.

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%I A126149 #30 Feb 16 2025 08:33:04
%S A126149 0,1,1,3,13,64,470,4921,83997,2411453,123544541,11537642646,
%T A126149 2013389528672
%N A126149 Number of connected nonhamiltonian graphs with n nodes.
%D A126149 J. P. Dolch, Names of Hamiltonian graphs, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 259-271.
%D A126149 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 219.
%H A126149 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], 2018-2019.
%H A126149 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NonhamiltonianGraph.html">Nonhamiltonian Graph</a>.
%F A126149 a(n) = A001349(n) - A003216(n).
%e A126149 a(10) = A001349(10) - A003216(10) = number of connected graphs on 10 unlabeled nodes - number of Hamiltonian graphs with 10 nodes = 11716571 - 9305118 = 2411453.
%e A126149 a(11) = A001349(11) - A003216(11) = number of connected graphs on 11 unlabeled nodes - number of Hamiltonian graphs with 11 nodes = 1006700565 - 883156024 = 123544541.
%Y A126149 Cf. A000088, A001349, A003216, A022564.
%Y A126149 Cf. A246446 (number of not-necessarily-connected simple nonhamiltonian graphs on n nodes).
%K A126149 nonn,more
%O A126149 1,4
%A A126149 _Jonathan Vos Post_, Mar 07 2007
%E A126149 Terms a(1)-a(9) corrected by _Travis Hoppe_, Jun 01 2014
%E A126149 a(11) added by _Eric W. Weisstein_, Aug 26 2014
%E A126149 a(12) from formula by _Falk Hüffner_, Aug 13 2017
%E A126149 a(13) added by _Jan Goedgebeur_, May 07 2019