A165134 Number of directed Hamiltonian paths in the n X n knight graph.
1, 0, 0, 0, 1728, 6637920, 165575218320, 19591828170979904
Offset: 1
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
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
Comments