A169773 Number of open knight's tour diagrams of a 3 X n chessboard that are symmetric under 180-degree rotation and have "type X": both endpoints occur in the same column.

0, 0, 0, 0, 0, 4, 0, 0, 0, 16, 0, 0, 0, 264, 0, 0, 0, 2144, 0, 0, 0, 22408, 0, 0, 0, 211808, 0, 0, 0, 2087344, 0, 0, 0, 20207664, 0, 0, 0, 197082624, 0, 0, 0, 1916054112, 0, 0, 0, 18652927040, 0, 0, 0, 181485750208, 0, 0, 0, 1766199186560, 0, 0, 0

Offset

4,6

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..60.

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

A169773(n)=0 unless n mod 4 = 1.

Crossrefs

Cf. A070030, A169696, A169764-A169777.

Sequence in context: A183099 A162296 A364103 * A236380 A298825 A265831

Adjacent sequences: A169770 A169771 A169772 * A169774 A169775 A169776

Keyword

nonn

Author

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

Extensions

a(31)-a(60) from Andrew Howroyd, Jul 01 2017

Status

approved