This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A169767 Number of closed knight's tour diagrams of a 3 X n chessboard that have "Eulerian symmetry". 3
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 124, 0, 0, 0, 1404, 0, 0, 0, 12824, 0, 0, 0, 126696, 0, 0, 0, 1222368, 0, 0, 0, 11930192, 0, 0, 0, 115974192, 0, 0, 0, 1128943296, 0, 0, 0, 10984783168, 0, 0, 0, 106897187552, 0, 0, 0, 1040241749856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,11 COMMENTS When the board is rotated 180 degrees, the diagram remains the same, and the second half of the tour is the same as the first half before rotation. (If the knight starts at one corner, he reaches the opposite corner after 3n/2 moves.) 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 A169767[n]=0 unless n mod 4 = 2. Generating function: (2*(8*z^14 + 14*z^18 - 182*z^22 - 168*z^26 + 348*z^30 - 1000*z^34 + 13224*z^38 + 22904*z^42 - 105776*z^46 - 111616*z^50 + 292800*z^54 + 217536*z^58 - 294656*z^62 - 114432*z^66 - 22528*z^70 - 44032*z^74 + 180224*z^78 - 65536*z^82 + 32768*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: A181029 A072838 A023919 * A225611 A173293 A008433 Adjacent sequences:  A169764 A169765 A169766 * A169768 A169769 A169770 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.