login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A169768 Number of geometrically distinct closed knight's tours of a 3 X n chessboard that have twofold symmetry. 2
0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 24, 0, 24, 0, 276, 0, 176, 0, 2604, 0, 1876, 0, 25736, 0, 17384, 0, 248816, 0, 173064, 0, 2424608, 0, 1668712, 0, 23581056, 0, 16317480, 0, 229513584, 0, 158435296, 0, 2233386048, 0, 1543447264, 0, 21733496960 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,7

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) = (A169765(n)+A169766(n)+A169767(n))/2.

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

Generating function: (4*z^10 + 24*z^16 - 124*z^18 + 32*z^20 + 212*z^22 - 716*z^24 + 1248*z^26 - 336*z^28 - 5120*z^30 + 7896*z^32 - 4928*z^34 - 3432*z^36 + 41280*z^38 - 32616*z^40 + 22224*z^42 + 39888*z^44 - 140608*z^46 + 47968*z^48 - 151680*z^50 - 143424*z^52 + 189952*z^54 - 15552*z^56 + 413056*z^58 + 181376*z^60 - 50432*z^62 + 78080*z^64 - 121344*z^66 + 44288*z^68 - 141312*z^70 - 112640*z^72 - 337920*z^74 - 227328*z^76 + 49152*z^78 + 98304*z^80 + 163840*z^82 + 32768*z^84 + 65536*z^86)/

(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: A265831 A264769 A169765 * A057386 A099306 A228630

Adjacent sequences:  A169765 A169766 A169767 * A169769 A169770 A169771

KEYWORD

nonn

AUTHOR

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 20 08:07 EST 2020. Contains 331081 sequences. (Running on oeis4.)