A003192 Length of uncrossed knight's path on an n X n board.

0, 0, 2, 5, 10, 17, 24, 35, 47

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• nice
• more
• hard

Comments

I used ZDD techniques to show that a(9)=47. (This is the longest uncrossed knight's path on a 9 X 9 board; thus I confirmed the conjecture that the paths of length 47, found by hand long ago, are indeed optimum.) - Don Knuth, Jun 24 2010

For best known results see link to Alex Chernov's site. - Dmitry Kamenetsky, Mar 02 2021

Examples

			Lengths of longest uncrossed knight's paths on all sufficiently small rectangular boards m X n, with 3 <= m <= n:
......2...4...5...6...8...9..10
..........5...7...9..11..13..15
.............10..14..16..19..22
.................17..21..25..29
.....................24..30..35
.........................35..42
.............................47
		

References

• D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, CSLI, Stanford, CA, 2010. (CSLI Lecture Notes, vol. 192)
• J. S. Madachy, Letter to N. J. A. Sloane, Apr 26 1975.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• Various authors, Uncrossed knight's tours, J. Rec. Math., 2 (1969), 154-157.
• L. D. Yarbrough, Uncrossed knight's tours, J. Rec. Math., 1 (No. 3, 1969), 140-142.

Links

• Alex Chernov, Uncrossed Knight's Tours.
• George Jelliss, Non-Intersecting Paths.
• J. S. Madachy, Letter to N. J. A. Sloane, Apr 26 1975.
• Jean-Charles Meyrignac, Non-crossing knight tours.
• N. J. A. Sloane, Illustration of initial terms
• Various authors, Uncrossed knight's tours, J. Rec. Math., 2 (1969), 154-157. [Annotated scanned copy]
• Eric Weisstein's World of Mathematics, Knight's Tour
• L. D. Yarbrough, Uncrossed knight's tours, J. Rec. Math., 1 (No. 3, 1969), 140-142. [Annotated scanned copy]

Crossrefs

Cf. A157416.

Extensions

a(1)=a(2)=0 prepended by Max Alekseyev, Jul 17 2011