login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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