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 A169764 Number of closed Knight's tours on a 3 X n board. 16
 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 176, 0, 1536, 0, 15424, 0, 147728, 0, 1448416, 0, 14060048, 0, 136947616, 0, 1332257856, 0, 12965578752, 0, 126169362176, 0, 1227776129152, 0, 11947846468608, 0, 116266505653888, 0, 1131418872918784, 0, 11010065269439104, 0, 107141489725900544 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS a(2n) = A070030(n), a(2n+1) = 0. A070030 is the main entry for this sequence. See that entry for much more information. 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 = 1..2031 (terms 1..1000 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 Asymptotic value .0001899*3.11949^n when n is even. Generating function: (16*z^10 + 80*z^12 - 544*z^14 - 1856*z^16 + 8080*z^18 + 9856*z^20 - 50864*z^22 - 64*z^24 + 152576*z^26 - 130816*z^28 - 214272*z^30 + 245760*z^32 + 222208*z^34 + 44544*z^36 - 53248*z^38 - 352256*z^40 + 81920*z^42 + 32768*z^44)/(1 - 6*z^2 - 64*z^4 + 200*z^6 + 1000*z^8 - 3016*z^10 - 3488*z^12 + 24256*z^14 - 23776*z^16 - 104168*z^18 + 203408*z^20 + 184704*z^22 - 443392*z^24 - 14336*z^26 + 151296*z^28 - 145920*z^30 + 263424*z^32 - 317440*z^34 - 36864*z^36 + 966656*z^38 - 573440*z^40 - 131072*z^42). MATHEMATICA CoefficientList[Series[(16*z^10 +80*z^12 -544*z^14 -1856*z^16 +8080*z^18 +9856*z^20 -50864*z^22 -64*z^24 +152576*z^26 -130816*z^28 -214272*z^30 +245760*z^32 +222208*z^34 +44544*z^36 -53248*z^38 -352256*z^40 +81920*z^42 +32768*z^44) / (1 -6*z^2 -64*z^4 +200*z^6 +1000*z^8 -3016*z^10 -3488*z^12 +24256*z^14 -23776*z^16 -104168*z^18 +203408*z^20 +184704*z^22 -443392*z^24 -14336*z^26 +151296*z^28 -145920*z^30 +263424*z^32 -317440*z^34 -36864*z^36 +966656*z^38 -573440*z^40 -131072*z^42), {z, 0, 50}], z] (* Harvey P. Dale, Feb 12 2013 *) CROSSREFS Cf. A070030, A169696, A169765-A169777. Sequence in context: A135925 A188784 A123935 * A002607 A221404 A221726 Adjacent sequences:  A169761 A169762 A169763 * A169765 A169766 A169767 KEYWORD nonn,easy 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 December 10 17:41 EST 2018. Contains 318049 sequences. (Running on oeis4.)