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A237429 Number of nonisomorphic Hamiltonian cycles on 2n X 2n square grid of points with exactly one axis of reflective symmetry. 2
0, 1, 19, 1394, 281990, 377205809, 1539951848735, 44222409563201991, 3842818845468254120853, 2396657968905952750257244144 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = A227257(n) - A237430(n).
EXAMPLE
The following two cycles with n=3 are counted only once, since they are isomorphic under the full symmetry group of the square. They have a horizontal and a vertical axis respectively. No example has a diagonal axis, since this brings other symmetries (see A063524).
o-o-o-o-o-o o-o o-o o-o
| | | | | | | |
o o-o-o-o-o o o o o o o
| | | | | | | |
o o-o-o-o-o o o o o o o
| | | | | | | |
o o-o-o-o-o o o o o o o
| | | | | | | |
o o-o-o o-o o o-o o-o o
| | | |
o-o-o-o-o-o o-o-o-o-o-o
CROSSREFS
Sequence in context: A130037 A047910 A357230 * A177611 A051847 A217830
KEYWORD
nonn,walk,more
AUTHOR
Ed Wynn, Feb 07 2014
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)