

A001230


Number of undirected closed knight's tours on a 2n X 2n chessboard.


9




OFFSET

1,3


COMMENTS

No closed tour exists on an m X m board if m is odd.


REFERENCES

Brendan McKay, personal communication, Feb 03, 1997.
W. W. Rouse Ball, Mathematical Recreations and Essays (various editions), Chap. 6.
I. Wegener, Branching Programs and Binary Decision Diagrams, SIAM, Philadelphia, 2000; see p. 369.


LINKS

Table of n, a(n) for n=1..4.
G. L. Chia, SiewHui Ong, Generalized knight's tour on rectangular chessboards, Disc. Appl. Math. 150(13) (2005) 8098
N. D. Elkies and R. P. Stanley, The mathematical knight, Math. Intelligencer, 25 (No. 1) (2003), 2234.
Brady Haran, Knight's Tour  Numberphile (2014)
George Jelliss, Knight's Tour Notes
Stoyan Kapralov, Valentin Bakoev, and Kaloyan Kapralov, Enumeration of Some Closed Knight Paths, arXiv preprint arXiv:1711.06792 [math.CO], 2017.
M. Loebbing and I. Wegener, The Number of Knight's Tours Equals 33,439,123,484,294  Counting with Binary Decision Diagrams. Electronic Journal of Combinatorics 3 (1996), R5. [The number given in the paper is incorrect, see comments.]
B. D. McKay, "Knight's Tours of an 8x8 Chessboard". Technical Report TRCS9703, Department of Computer Science, Australian National University (1997). [Cached copy, with permission]
Eric Weisstein's World of Mathematics, Hamiltonian Cycle and Knight Graph.
Wikipedia, Knight's tour


MATHEMATICA

Table[Length[FindHamiltonianCycle[KnightTourGraph[2 n, 2 n], All]], {n, 3}]


CROSSREFS

Cf. A165134.
Sequence in context: A203809 A257299 A208646 * A238076 A103810 A277944
Adjacent sequences: A001227 A001228 A001229 * A001231 A001232 A001233


KEYWORD

nonn,hard,more,nice


AUTHOR

N. J. A. Sloane, Martin Loebbing (loebbing(AT)ls2.informatik.unidortmund.de), Brendan McKay


EXTENSIONS

Loebbing and Wegener incorrectly gave 33439123484294 for the 8 X 8 board. The value given here is due to Brendan McKay and agrees with that given by Wegener in his book.
Description and links corrected by Max Alekseyev, Dec 09 2008


STATUS

approved



