
COMMENTS

I used ZDD techniques to show that a(9)=47. (This is the longest uncrossed knight 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


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.


EXAMPLE

Lengths of longest uncrossed knight 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
