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A249905
Smallest number of vertices supporting a graph with exactly n Hamiltonian cycles up to direction.
4
2, 1, 5, 4, 5, 6, 5, 6, 6, 7, 6, 7, 5, 8, 6, 7, 6, 7, 6, 7, 7, 8, 7, 7, 6, 8, 7, 7, 7, 8, 7, 8, 7, 7, 7, 8, 6, 8, 7, 8, 7, 8, 8, 8, 8, 7, 8, 8, 7, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 6, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 7, 8, 8, 8, 7, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9
OFFSET
0,1
COMMENTS
"Up to direction" means that cycles differing only in starting vertex or direction of traversal are treated as one cycle. a(n) always exists since the wheel graph on n spokes has n cycles.
LINKS
Andreas Björklund, Determinant Sums for Undirected Hamiltonicity, arXiv preprint arXiv:1008.0541 [cs.DS], 2010.
Erich Friedman, Math Magic (September 2012)
EXAMPLE
a(3) = 4 since K_4 has 3 Hamiltonian cycles up to direction.
CROSSREFS
Cf. A244511 (a(n) <= 7), A249906 (records), A305190.
Sequence in context: A266628 A283441 A262219 * A171175 A176053 A259791
KEYWORD
nonn,hard
AUTHOR
Jeremy Tan, Nov 08 2014
STATUS
approved