%I
%S 0,0,0,8,0,0,52,396,560,3048,10672,57248,128864,646272,1838784,
%T 8636880,23400992,105865688,305753680,1322849752,3862974304,
%U 16225820000,48744080192,198673312880,607041217056,2417584484232,7519864632928,29320809649000,92507134938336
%N Number of undirected Knight's tours on a 3 X n board.
%C I think the (old) name "Number of open Knight's tours on a 3 X n board" is somewhat incorrect, because included are those tours in which the start/end cells are knightneighbors. Such tours are potentially closed, although actually closing them would deprive them of specific start/end cells. "Number of undirected Knight's tours on a 3 X n board" would be a better name. For example the 3x10 has 3048 undirected tours, which would be 6096 directed tours, in accord with Colin Rose results (http://www.tri.org.au/knightframe.html, Solutions:3xm). Note that the 3x10 also has 16 closed tours (A169764 Number of closed Knight's tours on a 3 X n board), and each of those closed tour appears 30 times among the 3048 undirected tours, and 60 times among the 6096 directed tours.  _Pierre Charland_, Feb 15 2011
%D D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, to appear, 2010.
%H Seiichi Manyama, <a href="/A169696/b169696.txt">Table of n, a(n) for n = 1..1861</a>
%H George Jelliss, <a href="http://www.mayhematics.com/t/oa.htm">Open knight's tours of threerank boards</a>, Knight's Tour Notes, note 3a (21 October 2000).
%H George Jelliss, <a href="http://www.mayhematics.com/t/ob.htm">Closed knight's tours of threerank boards</a>, Knight's Tour Notes, note 3b (21 October 2000).
%H D. E. Knuth, <a href="/A169696/a169696.txt">Comments, generating function, first 100 terms</a>
%F a(n) = A169770(n) + A169771(n) + A169772(n).
%F Asymptotic value: 0.02789*3.45059^n.
%Y Cf. A118067.
%K nonn
%O 1,4
%A _N. J. A. Sloane_, Apr 14 2010, based on a communication from _Don Knuth_
