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 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

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