This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A169767 #13 Jul 22 2017 10:05:05 %S A169767 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, %T A169767 0,0,0,1222368,0,0,0,11930192,0,0,0,115974192,0,0,0,1128943296,0,0,0, %U A169767 10984783168,0,0,0,106897187552,0,0,0,1040241749856 %N A169767 Number of closed knight's tour diagrams of a 3 X n chessboard that have "Eulerian symmetry". %C A169767 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.) %D A169767 D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, to appear, 2010. %H A169767 Seiichi Manyama, <a href="/A169767/b169767.txt">Table of n, a(n) for n = 4..4057</a> %H A169767 George Jelliss, <a href="http://www.mayhematics.com/t/oa.htm">Open knight's tours of three-rank boards</a>, Knight's Tour Notes, note 3a (21 October 2000). %H A169767 George Jelliss, <a href="http://www.mayhematics.com/t/ob.htm">Closed knight's tours of three-rank boards</a>, Knight's Tour Notes, note 3b (21 October 2000). %F A169767 A169767[n]=0 unless n mod 4 = 2. %F A169767 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))/ %F A169767 (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). %Y A169767 Cf. A070030, A169696, A169764-A169777. %K A169767 nonn %O A169767 4,11 %A A169767 _N. J. A. Sloane_, May 10 2010, based on a communication from _Don Knuth_, Apr 28 2010