login
A165134
Number of directed Hamiltonian paths in the n X n knight graph.
7
1, 0, 0, 0, 1728, 6637920, 165575218320, 19591828170979904
OFFSET
1,5
COMMENTS
Previous name was: Number of knight's paths visiting each square of an n X n chessboard exactly once.
LINKS
Stefan Behnel, The Knight's Paths
P. Hingston, G. Kendall, Enumerating knight's tours using an ant colony algorithm, The 2005 IEEE Congress on Evolutionary Computation, 2 (2006), 1003-1010
G. Stertenbrink, Number of Knight's Tours
Eric Weisstein's World of Mathematics, Hamiltonian Path
Eric Weisstein's World of Mathematics, Knight Graph
EXAMPLE
From Gheorghe Coserea, Oct 08 2016: (Start)
For n=5 the numbers in the table below give the number of knight's paths starting at the respective position on the 5 X 5 chessboard. In total there are a(5) = 304*4 + 56*8 + 64 = 1728 solutions.
[1] [2] [3] [4] [5]
[1] 304 0 56 0 304
[2] 0 56 0 56 0
[3] 56 0 64 0 56
[4] 0 56 0 56 0
[5] 304 0 56 0 304
(End)
CROSSREFS
Cf. Undirected Hamiltonian paths: A169696 (3 X n), A079137 (4 X n), A083386 (5 X n), A306281 (6 X n), A306283 (7 X n), A308131 (n X n).
Sequence in context: A289209 A114767 A350384 * A013797 A344744 A013864
KEYWORD
nonn,hard,more
AUTHOR
[No name given] (c.candide(AT)free.fr), Sep 04 2009
EXTENSIONS
a(7) from Guenter Stertenbrink, added by Alex Chernov, Sep 01 2013
a(1)=1, a(2)=0 prepended by Max Alekseyev, Sep 22 2013
a(8) from Alex Chernov, May 10 2014
Name made more precise by Eric W. Weisstein, Apr 14 2019
STATUS
approved