A157416 Length of maximal uncrossed cycle of knight moves on n X n board.

0, 0, 0, 4, 8, 12, 24, 32, 42, 54

Offset: 1

Author

Don Knuth, Jun 24 2010

Keywords

• nonn
• more
• hard

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

Examples

			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
		

References

• D. E. Knuth, Selected Papers on Fun and Games. CSLI, Stanford, CA, 2010. (CSLI Lecture Notes, vol. 192)

Links

• Alex Chernov, Uncrossed Knight's Tours.

Crossrefs

Cf. A003192.

Extensions

a(1)=a(2)=a(3)=0 prepended by Max Alekseyev, Jul 17 2011