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 A326214 Number of labeled n-vertex digraphs (with loops) containing a (directed) Hamiltonian path. 6
 0, 0, 12, 384, 53184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A path is Hamiltonian if it passes through every vertex exactly once. LINKS Wikipedia, Hamiltonian path 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. Cf. A000595, A002416, A003024, A003216, A057864, A326224, A326225, A326226. Sequence in context: A251590 A196459 A193132 * A187513 A138914 A326220 Adjacent sequences:  A326211 A326212 A326213 * A326215 A326216 A326217 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 15 2019 STATUS approved

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Last modified September 23 04:19 EDT 2021. Contains 347609 sequences. (Running on oeis4.)