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

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

Table of n, a(n) for n=1..8.

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

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).

Cf. A001230, A118067, A306282.

Sequence in context: A289209 A114767 A350384 * A013797 A344744 A013864

Adjacent sequences: A165131 A165132 A165133 * A165135 A165136 A165137

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