OFFSET
4,11
COMMENTS
When the board is rotated 180 degrees, the diagram remains the same, and the second half of the tour is the same as the first half before rotation. (If the knight starts at one corner, he reaches the opposite corner after 3n/2 moves.)
REFERENCES
D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, to appear, 2010.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 4..4057
George Jelliss, Open knight's tours of three-rank boards, Knight's Tour Notes, note 3a (21 October 2000).
George Jelliss, Closed knight's tours of three-rank boards, Knight's Tour Notes, note 3b (21 October 2000).
FORMULA
A169767[n]=0 unless n mod 4 = 2.
Generating function: (2*(8*z^14 + 14*z^18 - 182*z^22 - 168*z^26 + 348*z^30 - 1000*z^34 + 13224*z^38 + 22904*z^42 - 105776*z^46 - 111616*z^50 + 292800*z^54 + 217536*z^58 - 294656*z^62 - 114432*z^66 - 22528*z^70 - 44032*z^74 + 180224*z^78 - 65536*z^82 + 32768*z^86))/
(1 - 6*z^4 - 64*z^8 + 200*z^12 + 1000*z^16 - 3016*z^20 - 3488*z^24 + 24256*z^28 - 23776*z^32 - 104168*z^36 + 203408*z^40 + 184704*z^44 - 443392*z^48 - 14336*z^52 + 151296*z^56 - 145920*z^60 + 263424*z^64 - 317440*z^68 - 36864*z^72 + 966656*z^76 - 573440*z^80 - 131072*z^84).
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 10 2010, based on a communication from Don Knuth, Apr 28 2010
STATUS
approved