OFFSET
0,1
COMMENTS
The reverse of a path is counted as the same path. a(n) is well-defined as the cycle graph C_n has n paths.
a(n) >= A249905(n) - 1, since the number of Hamiltonian paths in G is the same as the number of Hamiltonian cycles in H, where H is G with a new vertex connected to all vertices in G.
LINKS
Jeremy Tan, Table of n, a(n) for n = 0..2412
Erich Friedman, Math Magic (September 2012).
EXAMPLE
a(12) = 4 since K_4 has 12 Hamiltonian paths, and no graph on less than 4 vertices has 12 Hamiltonian paths.
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Jeremy Tan, Nov 14 2018
STATUS
approved