login
A363577
Number of inequivalent Hamiltonian paths starting in the lower left corner of an n X n grid graph (paths differing only by rotations and reflections are regarded as equivalent).
0
1, 1, 3, 23, 347, 10199, 683227, 85612967, 25777385143
OFFSET
1,3
COMMENTS
Equivalently, number of inequivalent Hamiltonian paths starting in a corner of an n X n grid graph (paths differing only by rotations and reflections are regarded as equivalent). - Martin Ehrenstein, Jul 08 2023
LINKS
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Hamiltonian Path
EXAMPLE
There are 3 paths for n=3:
+--+--+ +--+--+ +--+ +
| | | | | | |
+ + + + +--+ + + +
| | | | | | | |
+ +--+ + +--+ + +--+
A fourth path:
+--+--+
|
+--+ +
| | |
+ +--+
is the same as the second one in the row above after a 90-degree rotation.
All paths starting E are the same as the corresponding ones starting N after reflection in the forward diagonal.
KEYWORD
nonn,hard,walk,more
AUTHOR
Lars Blomberg, Jun 10 2023
EXTENSIONS
a(1) added by N. J. A. Sloane, Jun 10 2023
a(8)-a(9) from Martin Ehrenstein, Jul 08 2023
STATUS
approved