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%I #13 Jul 01 2017 22:59:33
%S 2,0,0,4,12,20,28,120,104,304,384,1304,1680,4936,5908,18304,21412,
%T 63440,76920,233248,281284,833720,990104,2993016,3523740,10485472,
%U 12432392,37485424,44184884,131430320,154630088,465106072,544994604,1622783328,1904647128
%N Number of open knight's tour diagrams of a 3 X n chessboard that are symmetric under 180-degree rotation and have "type F": the endpoints occur in different columns and agree in color with the cells in the nearest corner.
%D D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, to appear, 2010.
%H 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 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).
%H D. E. Knuth <a href="/A169770/a169770.txt">Generating functions for A169770-A169777 and A169696.</a>
%Y Cf. A070030, A169696, A169764-A169777.
%K nonn
%O 4,1
%A _N. J. A. Sloane_, May 10 2010, based on a communication from _Don Knuth_, Apr 28 2010
%E a(31)-a(38) from _Andrew Howroyd_, Jul 01 2017