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 A118067 Number of (directed) Hamiltonian paths in the 3 X n knight graph. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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]. REFERENCES Kraitchik, M., Mathematical Recreations. New York: W. W. Norton, pp. 264-5, 1942. LINKS 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 FORMULA a(n) = 2 * A169696(n). - Andrew Howroyd, Jul 01 2017 MATHEMATICA Mathematica notebook available at: http://www.tri.org.au/knightframe.html CROSSREFS 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 KEYWORD nonn AUTHOR Colin Rose, May 11 2006 EXTENSIONS 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 STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)