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

0, 0, 9862, 13267364410532

Offset: 1

Author

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

Keywords

• nonn
• hard
• more
• nice

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

Crossrefs

Cf. A165134.

Programs

Mathematica

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

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