A326221 Number of unlabeled n-vertex digraphs (with loops) containing a Hamiltonian path.

0, 0, 7, 74, 2395

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..4.

Wikipedia, Hamiltonian path

Gus Wiseman, Enumeration of paths and cycles and e-coefficients of incomparability graphs, arXiv:0709.0430 [math.CO], 2007.

Gus Wiseman, Non-isomorphic representatives of the a(3) = 74 digraphs containing a Hamiltonian path.

Formula

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

Crossrefs

The labeled case is A326214.

The undirected case is A057864 (without loops).

Unlabeled digraphs not containing a Hamiltonian path are A326224.

Unlabeled digraphs containing a Hamiltonian cycle are A326226.

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

Sequence in context: A054745 A323322 A356589 * A197091 A174243 A157706

Adjacent sequences: A326218 A326219 A326220 * A326222 A326223 A326224

Keyword

nonn,more

Author

Gus Wiseman, Jun 16 2019

Status

approved