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

4,1

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

Crossrefs

Cf. A070030, A169696, A169764-A169777.

Sequence in context: A228630 A174647 A258644 * A287633 A222931 A258645

Adjacent sequences: A169767 A169768 A169769 * A169771 A169772 A169773

Keyword

nonn

Author

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

Status

approved