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A326206
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Number of n-vertex labeled simple graphs containing a Hamiltonian path.
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10
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0, 0, 1, 4, 34, 633, 23368, 1699012, 237934760, 64558137140, 34126032806936, 35513501049012952
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OFFSET
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0,4
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COMMENTS
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A path is Hamiltonian if it passes through every vertex exactly once.
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LINKS
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Table of n, a(n) for n=0..11.
F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 9766535.
Wikipedia, Hamiltonian path
Gus Wiseman, Enumeration of paths and cycles and e-coefficients of incomparability graphs.
Gus Wiseman, The a(4) = 34 simple graphs containing a Hamiltonian path
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FORMULA
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A006125(n) = a(n) + A326205(n).
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MATHEMATICA
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Table[Length[Select[Subsets[Subsets[Range[n], {2}]], FindHamiltonianPath[Graph[Range[n], #]]!={}&]], {n, 0, 4}] (* Mathematica 10.2+ *)
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CROSSREFS
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The unlabeled case is A057864.
The directed case is A326214 (with loops) or A326217 (without loops).
Simple graphs without a Hamiltonian path are A326205.
Simple graphs with a Hamiltonian cycle are A326208.
Cf. A003216, A006125, A057864, A283420.
Sequence in context: A333981 A030243 A222789 * A088077 A162079 A353041
Adjacent sequences: A326203 A326204 A326205 * A326207 A326208 A326209
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KEYWORD
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nonn,more
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AUTHOR
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Gus Wiseman, Jun 14 2019
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EXTENSIONS
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a(7)-a(11) added using tinygraph by Falk Hüffner, Jun 21 2019
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STATUS
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approved
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