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A157416 Length of maximal uncrossed cycle of knight moves on n X n board. 1
0, 0, 0, 4, 8, 12, 24, 32, 42, 54 (list; graph; refs; listen; history; text; internal format)
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.

REFERENCES

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

LINKS

Table of n, a(n) for n=1..10.

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 * A059992 A050570 A233341

Adjacent sequences:  A157413 A157414 A157415 * A157417 A157418 A157419

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

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Last modified May 30 20:09 EDT 2016. Contains 273531 sequences.