A169775 Number of open knight's tour diagrams of a 3 X n chessboard that are symmetric under 180-degree rotation and have "type B": the endpoints occur in different columns and disagree in color with the cells in the nearest corner.

2, 0, 0, 0, 8, 0, 16, 0, 48, 0, 200, 0, 616, 0, 1832, 0, 6008, 0, 19304, 0, 62180, 0, 189580, 0, 615792, 0, 1895952, 0, 6136708, 0, 18699436, 0, 60490008, 0, 184450888, 0, 595959276, 0, 1811054676, 0, 5847417040, 0, 17754996288, 0, 57292227492

Offset

4,1

References

D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, to appear, 2010.

Links

Table of n, a(n) for n=4..48.

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

A169775(n)=0 unless n mod 2 = 0.

Crossrefs

Cf. A070030, A169696, A169764-A169777.

Sequence in context: A272822 A265663 A107491 * A329039 A365437 A390174

Adjacent sequences: A169772 A169773 A169774 * A169776 A169777 A169778

Keyword

nonn

Author

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

Extensions

a(31)-a(48) from Andrew Howroyd, Jul 01 2017

Status

approved