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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: A285340 A252798 A373736 * A003194 A350998 A352729 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 August 4 16:45 EDT 2024. Contains 374923 sequences. (Running on oeis4.)