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

4,1

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

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

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

Crossrefs

Cf. A070030, A169696, A169764-A169777.

Sequence in context: A372359 A057383 A218881 * A193542 A193545 A336399

Adjacent sequences: A169769 A169770 A169771 * A169773 A169774 A169775

Keyword

nonn

Author

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

Status

approved