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 A165134 Number of directed Hamiltonian paths in the n X n knight graph. 7

%I

%S 1,0,0,0,1728,6637920,165575218320,19591828170979904

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

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

%H Stefan Behnel, <a href="http://www.behnel.de/knight.html">The Knight's Paths</a>

%H A. Chernov, <a href="http://alex-black.ru/article.php?content=141">Open knight's tours</a>

%H Gheorghe Coserea, <a href="/A165134/a165134.txt">Solutions for 5x5 chessboard</a>

%H P. Hingston, G. Kendall, <a href="http://dx.doi.org/10.1109/CEC.2005.1554800">Enumerating knight's tours using an ant colony algorithm</a>, The 2005 IEEE Congress on Evolutionary Computation, 2 (2006), 1003-1010

%H G. Stertenbrink, <a href="http://magictour.free.fr/enum">Number of Knight's Tours</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>

%e From _Gheorghe Coserea_, Oct 08 2016: (Start)

%e 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.

%e [1] [2] [3] [4] [5]

%e [1] 304 0 56 0 304

%e [2] 0 56 0 56 0

%e [3] 56 0 64 0 56

%e [4] 0 56 0 56 0

%e [5] 304 0 56 0 304

%e (End)

%Y 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).

%Y Cf. A001230, A118067, A306282.

%K nonn,hard,more,changed

%O 1,5

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

%E a(7) from Guenter Stertenbrink, added by _Alex Chernov_, Sep 01 2013

%E a(1)=1, a(2)=0 prepended by _Max Alekseyev_, Sep 22 2013

%E a(8) from _Alex Chernov_, May 10 2014

%E Name made more precise by _Eric W. Weisstein_, Apr 14 2019

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)