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A157416
Length of maximal uncrossed cycle of knight moves on n X n board.
3
0, 0, 0, 4, 8, 12, 24, 32, 42, 54
OFFSET
1,4
COMMENTS
I had computed the values for n up to 8 long ago and reported them in a letter to the editor of the Journal of Recreational Mathematics 2 (1969), 155-157. The values for n=9 and n=10 are new, found using ZDDs.
For best known results see link to Alex Chernov's site. - Dmitry Kamenetsky, Mar 02 2021
REFERENCES
D. E. Knuth, Selected Papers on Fun and Games. CSLI, Stanford, CA, 2010. (CSLI Lecture Notes, vol. 192)
EXAMPLE
Lengths of longest uncrossed knight cycles on all sufficiently small rectangular boards m X n, with 3 <=m <= n:
......0...0...4...6...6...6...6..10
..........4...6...8..10..12..14..16
..............8..12..14..18..20..22
.................12..18..22..24..28
.....................24..26..32..36
.........................32..36..42
.............................42..50
.................................54
CROSSREFS
Cf. A003192.
Sequence in context: A014617 A239053 A272708 * A278602 A059992 A050570
KEYWORD
nonn,more,hard
AUTHOR
Don Knuth, Jun 24 2010
EXTENSIONS
a(1)=a(2)=a(3)=0 prepended by Max Alekseyev, Jul 17 2011
STATUS
approved