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A001230 Number of undirected closed knight's tours on a 2n X 2n chessboard. 8
0, 0, 9862, 13267364410532 (list; graph; refs; listen; history; text; internal format)



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


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.


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

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 and Knight Graph.

Wikipedia, Knight's tour


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


Cf. A165134.

Sequence in context: A203809 A257299 A208646 * A238076 A103810 A277944

Adjacent sequences:  A001227 A001228 A001229 * A001231 A001232 A001233




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


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



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Last modified December 15 20:32 EST 2017. Contains 296047 sequences.