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A001230 Number of undirected closed knight's tours on a 2n X 2n chessboard. 12
0, 0, 9862, 13267364410532 (list; graph; refs; listen; history; text; internal format)
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
G. L. Chia, Siew-Hui Ong, Generalized knight's tour on rectangular chessboards, Disc. Appl. Math. 150(1-3) (2005) 80-98.
N. D. Elkies and R. P. Stanley, The mathematical knight, Math. Intelligencer, 25 (No. 1) (2003), 22-34.
Brady Haran, Knight's Tour, Numberphile video (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 TR-CS-97-03, Department of Computer Science, Australian National University (1997). [Cached copy, with permission]
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
Eric Weisstein's World of Mathematics, 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
KEYWORD
nonn,hard,more,nice
AUTHOR
N. J. A. Sloane, Martin Loebbing (loebbing(AT)ls2.informatik.uni-dortmund.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

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Last modified April 16 22:26 EDT 2024. Contains 371755 sequences. (Running on oeis4.)