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A001230
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Number of closed knight's tours on a 2n X 2n chessboard.
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5
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OFFSET
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1,3
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COMMENTS
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No closed tour exists on an m X m board if m is odd.
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..4.
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.
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, Vol. 3, Paper 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).
Eric Weisstein's World of Mathematics, Knight's Tour
Wikipedia, Knight's tour
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CROSSREFS
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Sequence in context: A022199 A203809 A208646 * A103810 A205612 A205350
Adjacent sequences: A001227 A001228 A001229 * A001231 A001232 A001233
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KEYWORD
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nonn,hard,more,nice,changed
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AUTHOR
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N. J. A. Sloane, Martin Loebbing (loebbing(AT)ls2.informatik.uni-dortmund.de), Brendan McKay
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EXTENSIONS
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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. - Max Alekseyev, Dec 09 2008
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STATUS
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approved
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