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A326240
Number of Hamiltonian labeled n-vertex graphs with loops.
3
0, 2, 0, 8, 160, 6976, 644992
OFFSET
0,2
COMMENTS
A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once.
FORMULA
a(n) = A326208(n) * 2^n.
EXAMPLE
The a(3) = 8 edge-sets:
{12,13,23} {11,12,13,23} {11,12,13,22,23} {11,12,13,22,23,33}
{12,13,22,23} {11,12,13,23,33}
{12,13,23,33} {12,13,22,23,33}
MATHEMATICA
Table[Length[Select[Subsets[Select[Tuples[Range[n], 2], OrderedQ]], FindHamiltonianCycle[Graph[Range[n], #]]!={}&]], {n, 0, 5}]
CROSSREFS
The unlabeled case is A326215.
The directed case is A326204 (with loops) or A326219 (without loops).
The case without loops A326208.
Graphs with loops not containing a Hamiltonian cycle are A326239.
Sequence in context: A328920 A033836 A185159 * A009099 A193247 A373697
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 17 2019
STATUS
approved