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A118067
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Number of (directed) Hamiltonian paths in the 3 X n knight graph.
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6
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0, 0, 0, 16, 0, 0, 104, 792, 1120, 6096, 21344, 114496, 257728, 1292544, 3677568, 17273760, 46801984, 211731376, 611507360, 2645699504, 7725948608, 32451640000, 97488160384, 397346625760, 1214082434112, 4835168968464, 15039729265856, 58641619298000
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OFFSET
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1,4
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COMMENTS
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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].
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REFERENCES
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Kraitchik, M., Mathematical Recreations. New York: W. W. Norton, pp. 264-5, 1942.
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 1..1861
G. Jelliss, Open Knight's Tours of Three-Rank Boards
Seiichi Manyama calculated a(14)-a(21) by yoh2's code
C. Rose, The Distribution of the Knight.
Eric Weisstein's World of Mathematics, Hamiltonian Path
Eric Weisstein's World of Mathematics, Knight Graph
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FORMULA
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a(n) = 2 * A169696(n). - Andrew Howroyd, Jul 01 2017
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MATHEMATICA
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Mathematica notebook available at: http://www.tri.org.au/knightframe.html
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CROSSREFS
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Cf. A169696, A079137, A083386, A165134.
Cf. A158074. - Eric W. Weisstein, Mar 13 2009
Sequence in context: A008433 A347803 A010111 * A037217 A109075 A187585
Adjacent sequences: A118064 A118065 A118066 * A118068 A118069 A118070
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KEYWORD
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nonn
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AUTHOR
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Colin Rose, May 11 2006
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EXTENSIONS
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a(13) from Eric W. Weisstein, Mar 13 2009
a(14)-a(21) from Seiichi Manyama, Apr 25 2016
a(22)-a(28) from Andrew Howroyd, Jul 01 2017
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STATUS
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approved
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