|
%I #20 Jul 22 2017 10:04:41
%S 0,0,0,0,0,0,0,0,0,16,0,176,0,1536,0,15424,0,147728,0,1448416,0,
%T 14060048,0,136947616,0,1332257856,0,12965578752,0,126169362176,0,
%U 1227776129152,0,11947846468608,0,116266505653888,0,1131418872918784,0,11010065269439104,0,107141489725900544
%N Number of closed Knight's tours on a 3 X n board.
%C a(2n) = A070030(n), a(2n+1) = 0.
%C A070030 is the main entry for this sequence. See that entry for much more information.
%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="/A169764/b169764.txt">Table of n, a(n) for n = 1..2031</a> (terms 1..1000 from Alois P. Heinz)
%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).
%F Asymptotic value .0001899*3.11949^n when n is even.
%F 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).
%t 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 *)
%Y Cf. A070030, A169696, A169765-A169777.
%K nonn,easy
%O 1,10
%A _N. J. A. Sloane_, May 10 2010, based on a communication from _Don Knuth_, Apr 28 2010
|
