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A157460 Expansion of 88*x^2 / (1-483*x+483*x^2-x^3).

%I A157460 #18 Jul 25 2016 11:30:59
%S A157460 0,88,42504,20486928,9874656880,4759564129320,2294100035675448,
%T A157460 1105751457631436704,532969908478316815968,256890390135091073859960,
%U A157460 123820635075205419283684840,59681289215858877003662233008,28766257581408903510345912625104
%N A157460 Expansion of 88*x^2 / (1-483*x+483*x^2-x^3).
%C A157460 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 A157460     A    * c(n)+1 = a(n)^2,
%C A157460    (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
%C A157460 A157460 is the c(n) sequence for A=5.
%H A157460 Colin Barker, <a href="/A157460/b157460.txt">Table of n, a(n) for n = 1..350</a>
%H A157460 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (483,-483,1).
%F A157460 G.f.: 88*x^2 / (1-483*x+483*x^2-x^3).
%F A157460 c(1) = 0, c(2) = 88, c(3) = 483*c(2), c(n) = 483*(c(n-1)-c(n-2))+c(n-3) for n>3.
%F A157460 a(n) = -((241+44*sqrt(30))^(-n)*(-1+(241+44*sqrt(30))^n)*(11+2*sqrt(30)+(-11+2*sqrt(30))*(241+44*sqrt(30))^n))/120. - _Colin Barker_, Jul 25 2016
%t A157460 CoefficientList[Series[88x^2/(1-483x+483x^2-x^3),{x,0,30}],x] (* or *) LinearRecurrence[{483,-483,1},{0,0,88},30] (* _Harvey P. Dale_, Apr 16 2015 *)
%o A157460 (PARI) concat(0, Vec(88*x^2/(1-483*x+483*x^2-x^3)+O(x^20))) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A157460 (PARI) a(n) = round(-((241+44*sqrt(30))^(-n)*(-1+(241+44*sqrt(30))^n)*(11+2*sqrt(30)+(-11+2*sqrt(30))*(241+44*sqrt(30))^n))/120) \\ _Colin Barker_, Jul 25 2016
%Y A157460 5*A157460(n)+1 = A157014(n)^2 for n>=1.
%Y A157460 6*A157460(n)+1 = A133283(n)^2 for n>=1.
%K A157460 nonn,easy
%O A157460 1,2
%A A157460 _Paul Weisenhorn_, Mar 01 2009
%E A157460 Edited by _Alois P. Heinz_, Sep 09 2011