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A169777
Number of geometrically distinct open knight's tours of a 3 X n chessboard.
16
3, 0, 0, 14, 104, 146, 773, 2698, 14350, 32296, 161714, 460022, 2159794, 5851548, 26468357, 76442996, 330719293, 965759972, 4056479056, 12186078360, 49668414086, 151760518296, 604396415979, 1879966906486, 7330203447133, 23126786408904, 88609897281582
OFFSET
4,1
REFERENCES
D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, to appear, 2010.
LINKS
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
a(n) = A169696(n)/4 + A169776(n)/2.
EXAMPLE
The three distinct 3x4 tours were published by Euler in Memoires Acad. Roy. Sci. (Berlin, 1759), 310-337.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 10 2010, based on a communication from Don Knuth, Apr 28 2010
STATUS
approved