cp's OEIS Frontend

A169769 Number of geometrically distinct closed knight's tours of a 3 X n chessboard.

%I A169769 #19 Jul 22 2017 12:56:39
%S A169769 0,0,0,0,0,0,6,0,44,0,396,0,3868,0,37070,0,362192,0,3516314,0,
%T A169769 34237842,0,333077332,0,3241403380,0,31542464952,0,306944118820,0,
%U A169769 2986962829456,0,29066627247828,0,282854730020224,0,2752516325518516,0
%N A169769 Number of geometrically distinct closed knight's tours of a 3 X n chessboard.
%D A169769 D. E. Knuth, Long and skinny knight's tours, in Selected Papers on Fun and Games, to appear, 2010.
%H A169769 Seiichi Manyama, <a href="/A169769/b169769.txt">Table of n, a(n) for n = 4..2031</a> (terms 4..1000 from Alois P. Heinz)
%H A169769 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 A169769 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 A169769 a(n) = A169764(n)/4 + A169768(n)/2.
%F A169769 a(n) = 0 unless n mod 2 = 0.
%F A169769 Generating function: 2*z^10*((-2*(1 + 5*z^2 - 34*z^4 - 116*z^6 + 505*z^8 + 616*z^10 - 3179*z^12 - 4*z^14 + 9536*z^16 - 8176*z^18 - 13392*z^20 + 15360*z^22 + 13888*z^24 + 2784*z^26 - 3328*z^28 - 22016*z^30 + 5120*z^32 + 2048*z^34))/
%F A169769 (-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) -
%F A169769 (1 + 6*z^6 - 31*z^8 + 8*z^10 + 53*z^12 - 179*z^14 + 312*z^16 - 84*z^18 - 1280*z^20 + 1974*z^22 - 1232*z^24 - 858*z^26 + 10320*z^28 - 8154*z^30 + 5556*z^32 + 9972*z^34 - 35152*z^36 + 11992*z^38 - 37920*z^40 - 35856*z^42 + 47488*z^44 - 3888*z^46 + 103264*z^48 + 45344*z^50 - 12608*z^52 + 19520*z^54 - 30336*z^56 + 11072*z^58 - 35328*z^60 - 28160*z^62 - 84480*z^64 - 56832*z^66 + 12288*z^68 + 24576*z^70 + 40960*z^72 + 8192*z^74 + 16384*z^76)/
%F A169769 (-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)).
%e A169769 The six solutions for n=10 were first published by Kraitchik in 1927.
%Y A169769 Cf. A070030, A169696, A169764-A169777.
%K A169769 nonn
%O A169769 4,7
%A A169769 _N. J. A. Sloane_, May 10 2010, based on a communication from _Don Knuth_, Apr 28 2010
%E A169769 More terms from _R. J. Mathar_, Oct 09 2010