

A118067


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


4



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

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. 2645, 1942.


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1861
G. Jelliss, Open Knight's Tours of ThreeRank 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: A173293 A008433 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



