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A118067 Number of (directed) Hamiltonian paths in the 3 X n knight graph. 4


%S 0,0,0,16,0,0,104,792,1120,6096,21344,114496,257728,1292544,3677568,

%T 17273760,46801984,211731376,611507360,2645699504,7725948608,

%U 32451640000,97488160384,397346625760,1214082434112,4835168968464,15039729265856,58641619298000

%N Number of (directed) Hamiltonian paths in the 3 X n knight graph.

%C 1. Jelliss computes the number of tour diagrams (which is equal to half the number of tours). 2. Sequence A079137 computes the number of tour DIAGRAMS for a 4 X k board (again, equal to half the number of tours). 3. Kraitchik (1942) incorrectly reports 376 tour diagrams for the 3 X 8 case; the correct number is 396 (i.e., 792 tours) [cf. Rose, Jelliss].

%D Kraitchik, M., Mathematical Recreations. New York: W. W. Norton, pp. 264-5, 1942.

%H Seiichi Manyama, <a href="/A118067/b118067.txt">Table of n, a(n) for n = 1..1861</a>

%H G. Jelliss, <a href="http://www.mayhematics.com/t/oa.htm">Open Knight's Tours of Three-Rank Boards</a>

%H Seiichi Manyama calculated a(14)-a(21) by <a href="http://ja.stackoverflow.com/questions/16525/m%C3%97n-board">yoh2's code</a>

%H C. Rose, <a href="http://www.tri.org.au/knightframe.html">The Distribution of the Knight</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>

%F a(n) = 2 * A169696(n). - _Andrew Howroyd_, Jul 01 2017

%t Mathematica notebook available at: http://www.tri.org.au/knightframe.html

%Y Cf. A169696, A079137, A083386, A165134.

%Y Cf. A158074. - _Eric W. Weisstein_, Mar 13 2009

%K nonn

%O 1,4

%A _Colin Rose_, May 11 2006

%E a(13) from _Eric W. Weisstein_, Mar 13 2009

%E a(14)-a(21) from _Seiichi Manyama_, Apr 25 2016

%E a(22)-a(28) from _Andrew Howroyd_, Jul 01 2017

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)