A169770 Number of open knight's tour diagrams of a 3 X n chessboard that have "type X": both endpoints occur in the same column.

4, 0, 0, 0, 80, 40, 368, 352, 5296, 3744, 48656, 40208, 523808, 415488, 5270976, 4333504, 54215264, 44497728, 551297184, 458337984, 5613555008, 4691821600, 56981627840, 47988689152, 577641089664, 489273948160, 5845628996352

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

Asymptotic value 0.000169*n*3.11949^n when n is even, 0.0000526*n*3.11949^n when n is odd.