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 A326216 Number of labeled n-vertex digraphs (without loops) not containing a (directed) Hamiltonian path. 6
 1, 1, 1, 16, 772 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A path is Hamiltonian if it passes through every vertex exactly once. LINKS Wikipedia, Hamiltonian path FORMULA A053763(n) = a(n) + A326217(n). EXAMPLE The a(3) = 16 edge-sets:   {}  {12}  {12,13}       {13}  {12,21}       {21}  {12,32}       {23}  {13,23}       {31}  {13,31}       {32}  {21,23}             {21,31}             {23,32}             {31,32} MATHEMATICA Table[Length[Select[Subsets[Select[Tuples[Range[n], 2], UnsameQ@@#&]], FindHamiltonianPath[Graph[Range[n], DirectedEdge@@@#]]=={}&]], {n, 4}] (* Mathematica 10.2+ *) CROSSREFS Unlabeled digraphs not containing a Hamiltonian path are A326224. The undirected case is A326205. The unlabeled undirected case is A283420. The case with loops is A326213. Digraphs (without loops) containing a Hamiltonian path are A326217. Digraphs (without loops) not containing a Hamiltonian cycle are A326218. Cf. A000595, A002416, A003024, A003216, A057864, A326206, A326214, A326220, A326221, A326225. Sequence in context: A134183 A042109 A221061 * A194610 A215171 A224736 Adjacent sequences:  A326213 A326214 A326215 * A326217 A326218 A326219 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 15 2019 STATUS approved

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Last modified January 19 23:47 EST 2022. Contains 350467 sequences. (Running on oeis4.)