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

1,4

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