A165134 Number of directed Hamiltonian paths in the n X n knight graph.

1, 0, 0, 0, 1728, 6637920, 165575218320, 19591828170979904

Offset: 1

Author

[No name given] (c.candide(AT)free.fr), Sep 04 2009

Keywords

• nonn
• hard
• more

Comments

Previous name was: Number of knight's paths visiting each square of an n X n chessboard exactly once.

Examples

			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)
		

Links

• Stefan Behnel, The Knight's Paths
• A. Chernov, Open knight's tours
• Gheorghe Coserea, Solutions for 5x5 chessboard
• 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

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).

Cf. A001230, A118067, A306282.

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