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A001230 Number of undirected closed knight's tours on a 2n X 2n chessboard. 6
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

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.

Brady Haran, Knight's Tour - Numberphile (2014)

George Jelliss, Knight's Tour Notes

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).

Eric Weisstein's World of Mathematics, Hamiltonian Cycle

Eric Weisstein's World of Mathematics, Knight Graph

Wikipedia, Knight's tour

CROSSREFS

Cf. A165134.

Sequence in context: A022199 A203809 A208646 * A238076 A103810 A237917

Adjacent sequences:  A001227 A001228 A001229 * A001231 A001232 A001233

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. - Max Alekseyev, Dec 09 2008

STATUS

approved

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Last modified November 23 17:17 EST 2014. Contains 249851 sequences.