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A326214
Number of labeled n-vertex digraphs (with loops) containing a (directed) Hamiltonian path.
6
0, 0, 12, 384, 53184
OFFSET
0,3
COMMENTS
A path is Hamiltonian if it passes through every vertex exactly once.
FORMULA
A002416(n) = a(n) + A326213(n).
EXAMPLE
The a(2) = 12 edge-sets:
{12}
{21}
{11,12}
{11,21}
{12,21}
{12,22}
{21,22}
{11,12,21}
{11,12,22}
{11,21,22}
{12,21,22}
{11,12,21,22}
MATHEMATICA
Table[Length[Select[Subsets[Tuples[Range[n], 2]], FindHamiltonianPath[Graph[Range[n], DirectedEdge@@@#]]!={}&]], {n, 4}] (* Mathematica 10.2+ *)
CROSSREFS
The unlabeled case is A326221.
The undirected case is A326206.
The case without loops is A326217.
Digraphs not containing a Hamiltonian path are A326213.
Digraphs containing a Hamiltonian cycle are A326204.
Sequence in context: A352651 A196459 A193132 * A187513 A138914 A326220
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 15 2019
STATUS
approved