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%I A326205 #14 Aug 23 2023 08:43:12
%S A326205 1,1,1,4,30,391,9400,398140,30500696,4161339596,1058339281896,
%T A326205 515295969951016
%N A326205 Number of n-vertex labeled simple graphs not containing a Hamiltonian path.
%C A326205 A path is Hamiltonian if it passes through every vertex exactly once.
%H A326205 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian path</a>
%H A326205 Gus Wiseman, <a href="http://arxiv.org/abs/0709.0430">Enumeration of paths and cycles and e-coefficients of incomparability graphs</a>, arXiv:0709.0430 [math.CO], 2007.
%H A326205 Gus Wiseman, <a href="/A326205/a326205.png">The a(4) = 30 simple graphs not containing a Hamiltonian path</a>.
%F A326205 A006125(n) = a(n) + A326206(n).
%t A326205 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],FindHamiltonianPath[Graph[Range[n],#]]=={}&]],{n,0,4}] (* Mathematica 10.2+ *)
%Y A326205 The unlabeled case is A283420.
%Y A326205 The case for digraphs is A326213 (without loops) or A326216 (with loops).
%Y A326205 Simple graphs with a Hamiltonian path are A326206.
%Y A326205 Simple graphs without a Hamiltonian cycle are A326207.
%Y A326205 Cf. A003216, A006125, A057864.
%K A326205 nonn,more
%O A326205 0,4
%A A326205 _Gus Wiseman_, Jun 14 2019
%E A326205 a(7)-a(11) added from formula by _Falk Hüffner_, Jun 21 2019

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