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A326205
Number of n-vertex labeled simple graphs not containing a Hamiltonian path.
8
1, 1, 1, 4, 30, 391, 9400, 398140, 30500696, 4161339596, 1058339281896, 515295969951016
OFFSET
0,4
COMMENTS
A path is Hamiltonian if it passes through every vertex exactly once.
FORMULA
A006125(n) = a(n) + A326206(n).
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], FindHamiltonianPath[Graph[Range[n], #]]=={}&]], {n, 0, 4}] (* Mathematica 10.2+ *)
CROSSREFS
The unlabeled case is A283420.
The case for digraphs is A326213 (without loops) or A326216 (with loops).
Simple graphs with a Hamiltonian path are A326206.
Simple graphs without a Hamiltonian cycle are A326207.
Sequence in context: A187736 A199569 A363911 * A351795 A290058 A168129
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 14 2019
EXTENSIONS
a(7)-a(11) added from formula by Falk Hüffner, Jun 21 2019
STATUS
approved