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 A169765 Number of closed knight's tour diagrams of a 3 X n chessboard that are symmetric with respect to left-right reflection about a vertical axis. 4
 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 24, 0, 0, 0, 276, 0, 0, 0, 2604, 0, 0, 0, 25736, 0, 0, 0, 248816, 0, 0, 0, 2424608, 0, 0, 0, 23581056, 0, 0, 0, 229513584, 0, 0, 0, 2233386048, 0, 0, 0, 21733496960, 0, 0, 0, 211495383968, 0, 0, 0, 2058092298080 (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 (terms 4..1002 from Alois P. Heinz) 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 A169765(n)=0 unless n mod 4 = 2. And if n mod = 2, A169765(n) = A169765(n) + A169767(n). Generating function: (2*(2*z^10 - 62*z^18 + 106*z^22 + 624*z^26 - 2560*z^30 - 2464*z^34 + 20640*z^38 + 11112*z^42 - 70304*z^46 - 75840*z^50 + 94976*z^54 + 206528*z^58 - 25216*z^62 - 60672*z^66 - 70656*z^70 - 168960*z^74 + 24576*z^78 + 81920*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). EXAMPLE The first example, for n=10, was exhibited by Ernest Bergholt in British Chess Magazine 1918, page 74. CROSSREFS Cf. A070030, A169696, A169764-A169777. Sequence in context: A298825 A265831 A264769 * A169768 A057386 A099306 Adjacent sequences:  A169762 A169763 A169764 * A169766 A169767 A169768 KEYWORD nonn AUTHOR N. J. A. Sloane, May 10 2010, based on a communication from Don Knuth, Apr 28 2010 EXTENSIONS More terms from Alois P. Heinz, Nov 26 2010 STATUS approved

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)