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%I #12 Jul 25 2016 08:43:30
%S 0,104,70200,47314800,31890105104,21493883525400,14486845606014600,
%T 9764112444570315104,6580997300794786365600,4435582416623241440099400,
%U 2989575967806763935840630104,2014969766719342269515144590800,1358086633192868882889271613569200
%N Expansion of 104*x^2 / (-x^3+675*x^2-675*x+1).
%C This sequence is part of a solution of a more general problem involving two equations, three sequences a(n), b(n), c(n) and a constant A:
%C A * c(n)+1 = a(n)^2,
%C (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
%C A157874 is the c(n) sequence for A=6.
%H Colin Barker, <a href="/A157874/b157874.txt">Table of n, a(n) for n = 1..350</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (675,-675,1).
%F G.f.: 104*x^2 / (-x^3+675*x^2-675*x+1).
%F c(1) = 0, c(2) = 104, c(3) = 675*c(2), c(n) = 675 * (c(n-1)-c(n-2)) + c(n-3) for n>3.
%F a(n) = -((337+52*sqrt(42))^(-n)*(-1+(337+52*sqrt(42))^n)*(13+2*sqrt(42)+(-13+2*sqrt(42))*(337+52*sqrt(42))^n))/168. - _Colin Barker_, Jul 25 2016
%t Rest[CoefficientList[Series[104x^2/(-x^3+675x^2-675x+1),{x,0,20}],x]] (* or *) LinearRecurrence[{675,-675,1},{0,104,70200},20] (* _Harvey P. Dale_, Oct 04 2015 *)
%o (PARI) concat(0, Vec(104*x^2/(-x^3+675*x^2-675*x+1) + O(x^20))) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (PARI) a(n) = -round((337+52*sqrt(42))^(-n)*(-1+(337+52*sqrt(42))^n)*(13+2*sqrt(42)+(-13+2*sqrt(42))*(337+52*sqrt(42))^n))/168 \\ _Colin Barker_, Jul 25 2016
%Y 6*A157874(n)+1 = A153111(n)^2.
%Y 7*A157874(n)+1 = A157461(n)^2.
%K nonn,easy
%O 1,2
%A _Paul Weisenhorn_, Mar 08 2009
%E Edited by _Alois P. Heinz_, Sep 09 2011
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