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A169766 Number of closed knight's tour diagrams of a 3 X n chessboard that have "Bergholtian symmetry". 2
0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 48, 0, 152, 0, 352, 0, 1200, 0, 3752, 0, 12912, 0, 34768, 0, 122120, 0, 346128, 0, 1202240, 0, 3337424, 0, 11650864, 0, 32634960, 0, 113539392, 0, 316870592, 0, 1104442752, 0, 3086894528, 0, 10748713792, 0, 30023935744, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,7

COMMENTS

When the board is rotated 180 degrees, the diagram remains the same, but the tour reverses direction.

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..4057

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).

FORMULA

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

Generating function: (2*(2*z^10 - 8*z^14 + 24*z^16 - 76*z^18 + 32*z^20 + 288*z^22 - 716*z^24 + 792*z^26 - 336*z^28 - 2908*z^30 + 7896*z^32 - 1464*z^34 - 3432*z^36 + 7416*z^38 - 32616*z^40 - 11792*z^42 + 39888*z^44 + 35472*z^46 + 47968*z^48 + 35776*z^50 - 143424*z^52 - 197824*z^54 - 15552*z^56 - 11008*z^58 + 181376*z^60 + 269440*z^62 + 78080*z^64 + 53760*z^66 + 44288*z^68 - 48128*z^70 - 112640*z^72 - 124928*z^74 - 227328*z^76 - 155648*z^78 + 98304*z^80 + 147456*z^82 + 32768*z^84))/

(1 - 6*z^4 - 64*z^8 + 200*z^12 + 1000*z^16 - 3016*z^20 - 3488*z^24 + 24256*z^28 - 23776*z^32 - 104168*z^36 + 203408*z^40 + 184704*z^44 - 443392*z^48 - 14336*z^52 + 151296*z^56 - 145920*z^60 + 263424*z^64 - 317440*z^68 - 36864*z^72 + 966656*z^76 - 573440*z^80 - 131072*z^84)

CROSSREFS

Cf. A070030, A169696, A169764-A169777.

Sequence in context: A285214 A285340 A252798 * A003194 A286875 A105570

Adjacent sequences:  A169763 A169764 A169765 * A169767 A169768 A169769

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

More terms extracted from the g.f. by R. J. Mathar, Oct 09 2010

STATUS

approved

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)