

A003192


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


11




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), 154157.
L. D. Yarbrough, Uncrossed knight's tours, J. Rec. Math., 1 (No. 3, 1969), 140142.


LINKS



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



KEYWORD

nonn,walk,nice,more,hard


AUTHOR



EXTENSIONS



STATUS

approved



