A326221 - OEIS

%I #8 Aug 23 2023 08:43:21

%S 0,0,7,74,2395

%N Number of unlabeled n-vertex digraphs (with loops) containing a Hamiltonian path.

%C A directed path is Hamiltonian if it passes through every vertex exactly once.

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

%H 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 Gus Wiseman, <a href="/A326221/a326221.png">Non-isomorphic representatives of the a(3) = 74 digraphs containing a Hamiltonian path</a>.

%F A000595(n) = a(n) + A326224(n).

%Y The labeled case is A326214.

%Y The undirected case is A057864 (without loops).

%Y Unlabeled digraphs not containing a Hamiltonian path are A326224.

%Y Unlabeled digraphs containing a Hamiltonian cycle are A326226.

%Y Cf. A000595, A002416, A003087, A003216, A283420.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Jun 16 2019