A169772 Number of open knight's tour diagrams of a 3 X n chessboard that have "type B": the endpoints occur in different columns and disagree in color with the cells in the nearest corner.

2, 0, 0, 0, 92, 0, 1064, 0, 14928, 0, 156416, 0, 1785600, 0, 19416704, 0, 211014544, 0, 2261999424, 0, 24067157192, 0, 254242274472, 0, 2669251156032, 0, 27880294589248

Offset: 4

Author

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

Keywords

• nonn

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.

Crossrefs

Cf. A070030, A169696, A169764-A169777.

Formula

A169772(n)=0 unless n mod 2 = 0.

Asymptotic value: 0.00144*n*3.11949^n when n is even.