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A237432 Number of nonisomorphic Hamiltonian cycles on (4n-2) X (4n-2) square grid of points with four-fold rotational symmetry (and no other symmetry). 2
0, 1, 102, 255359, 15504309761, 21955745395591600, 712319733455900182066337, 524246290066954425217045809870657 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
For square grids of m X m points, there are solutions only for m = (4n-2).
LINKS
FORMULA
a(n) = A238819(n-1) / 2 for n > 1. - Andrew Howroyd, Apr 06 2016
EXAMPLE
The two cycles counted as a single class for n=2. These are isomorphic (here meaning isomorphic under the full symmetry group of the square), since each is a reflection of the other.
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: A353142 A129751 A225993 * A370404 A279242 A094095
KEYWORD
nonn,walk,hard,more
AUTHOR
Ed Wynn, Feb 07 2014
EXTENSIONS
a(6)-a(8) from Andrew Howroyd, Apr 06 2016
STATUS
approved

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Last modified March 29 08:08 EDT 2024. Contains 371265 sequences. (Running on oeis4.)