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

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

Offset: 1

Author

Colin Rose, May 11 2006

Keywords

• nonn

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

Crossrefs

Cf. A169696, A079137, A083386, A165134.

Cf. A158074. - Eric W. Weisstein, Mar 13 2009

Programs

Mathematica

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

Formula

a(n) = 2 * A169696(n). - Andrew Howroyd, Jul 01 2017

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