A246446 - OEIS

%I #21 Jan 02 2020 08:24:13

%S 0,2,3,8,26,108,661,6150,97585,2700050,135841840,12568984762,

%T 2179513027405

%N Number of nonhamiltonian graphs with n nodes.

%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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NonhamiltonianGraph.html">Nonhamiltonian Graph</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>

%F a(n) = A000088(n) - A003216(n).

%t A000088 = Cases[Import["https://oeis.org/A000088/b000088.txt", "Table"], {_, _}][[All, 2]];

%t A003216 = Cases[Import["https://oeis.org/A003216/b003216.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := A000088[[n + 1]] - A003216[[n]];

%t a /@ Range[13] (* _Jean-François Alcover_, Jan 02 2020 *)

%Y Cf. A000088 (number of simple graphs on n nodes).

%Y Cf. A003216 (number of Hamiltonian graphs on n nodes).

%Y Cf. A126149 (number of connected nonhamiltonian graphs on n nodes).

%Y The labeled case is A326207.

%Y The directed case is A326223 (with loops) or A326222 (without loops).

%Y Unlabeled simple graphs not containing a Hamiltonian path are A283420.

%Y Cf. A006125, A057864, A326205, A326206.

%K nonn,more

%O 1,2

%A _Eric W. Weisstein_, Aug 26 2014

%E a(12) from formula by _Falk Hüffner_, Aug 13 2017

%E a(13) added by _Jan Goedgebeur_, May 07 2019