A169771 Number of open knight's tour diagrams of a 3 X n chessboard that have "type F": the endpoints occur in different columns and agree in color with the cells in the nearest corner.

2, 0, 0, 52, 224, 520, 1616, 10320, 37024, 125120, 441200, 1798576, 6327472, 22985504, 81178008, 301420176, 1057619944, 3818476576, 13412523392, 48285742208, 168992600680, 602349395456, 2106360581920, 7471875943776, 26073917403304, 92017860990176, 320713651212384

Offset

4,1

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..1000

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).

D. E. Knuth Generating functions for A169770-A169777 and A169696.

Formula

Asymptotic value: 0.02789*3.45059^n.

Crossrefs

Cf. A070030, A169696, A169764-A169777.

Sequence in context: A013416 A365973 A156433 * A365982 A326779 A365981

Adjacent sequences: A169768 A169769 A169770 * A169772 A169773 A169774

Keyword

nonn

Author

N. J. A. Sloane, May 10 2010, based on a communication from Don Knuth, Apr 28 2010

Status

approved