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%I #18 Nov 06 2019 01:10:59
%S 0,0,2,36,560,8160,116192,1638336,23006720,322513920,4517714432,
%T 63263118336,885774356480,12401385185280,173622657769472,
%U 2430736799809536,34030432743587840,476426763687690240,6669978923292557312,93379730316084903936,1307316376765123788800
%N Number of n-move rook paths on 8 X 8 board from given corner to opposite corner.
%C Paths are not required to be self-avoiding. - _Andrew Howroyd_, Nov 05 2019
%H Andrew Howroyd, <a href="/A025608/b025608.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-44,-168).
%F G.f.: (2*x^2)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)).
%F a(0)=0, a(1)=0, a(2)=2, a(n)=18*a(n-1)-44*a(n-2)-168*a(n-3). - _Harvey P. Dale_, Mar 09 2013
%t CoefficientList[Series[(2x^2)/((1+2x)(1-6x)(1-14x)),{x,0,30}],x] (* or *) LinearRecurrence[{18,-44,-168},{0,0,2},30] (* _Harvey P. Dale_, Mar 09 2013 *)
%o (PARI) concat([0, 0], Vec(2/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)) + O(x^20))) \\ _Andrew Howroyd_, Nov 05 2019
%Y Cf. A025607, A025609.
%K nonn,walk
%O 0,3
%A _David W. Wilson_
%E More terms from _Harvey P. Dale_, Mar 09 2013
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