A003192 Length of uncrossed knight's path on an n X n board. (Formerly M1369)

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

Offset

1,3

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

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

Table of n, a(n) for n=1..9.

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]

Example

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

Crossrefs

Cf. A157416.

Sequence in context: A077166 A230429 A340039 * A018682 A078393 A340045

Adjacent sequences: A003189 A003190 A003191 * A003193 A003194 A003195

Keyword

nonn,walk,nice,more,hard

Author

N. J. A. Sloane

Extensions

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

Status

approved