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A157879 Expansion of 120*x^2 / (-x^3+899*x^2-899*x+1).

%I A157879 #22 Jul 25 2016 07:20:05
%S A157879 0,120,107880,96876240,86994755760,78121193796360,70152745034375640,
%T A157879 62997086919675528480,56571313901123590199520,
%U A157879 50800976886122064323640600,45619220672423712639039059400,40966009362859607827792751700720,36787430788627255405645251988187280
%N A157879 Expansion of 120*x^2 / (-x^3+899*x^2-899*x+1).
%C A157879 This sequence is part of a solution of a more general problem involving 2 equations, three sequences a(n), b(n), c(n) and a constant A:
%C A157879     A    * c(n)+1 = a(n)^2,
%C A157879    (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
%C A157879 A157879 is the c(n) sequence for A=7.
%H A157879 Colin Barker, <a href="/A157879/b157879.txt">Table of n, a(n) for n = 1..300</a>
%H A157879 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (899,-899,1).
%F A157879 G.f.: 120*x^2/(-x^3+899*x^2-899*x+1).
%F A157879 c(1) = 0, c(2) = 120, c(3) = 899*c(2), c(n) = 899 * (c(n-1)-c(n-2)) + c(n-3) for n>3.
%F A157879 a(n) = -((449+120*sqrt(14))^(-n)*(-1+(449+120*sqrt(14))^n)*(15+4*sqrt(14)+(-15+4*sqrt(14))*(449+120*sqrt(14))^n))/224. - _Colin Barker_, Jul 25 2016
%t A157879 CoefficientList[Series[120x^2/(-x^3+899x^2-899x+1),{x,0,30}],x] (* or *) LinearRecurrence[{899,-899,1},{0,0,120},30] (* _Harvey P. Dale_, Jan 14 2014 *)
%o A157879 (PARI) concat(0, Vec(120*x^2/(-x^3+899*x^2-899*x+1)+O(x^20))) \\ _Charles R Greathouse IV_, Sep 25 2012
%o A157879 (PARI) a(n) = round(-((449+120*sqrt(14))^(-n)*(-1+(449+120*sqrt(14))^n)*(15+4*sqrt(14)+(-15+4*sqrt(14))*(449+120*sqrt(14))^n))/224) \\ _Colin Barker_, Jul 25 2016
%Y A157879 7*A157879(n)+1 = A157877(n)^2.
%Y A157879 8*A157879(n)+1 = A157878(n)^2.
%Y A157879 Cf. A245031.
%K A157879 nonn,easy
%O A157879 1,2
%A A157879 _Paul Weisenhorn_, Mar 08 2009
%E A157879 Edited by _Alois P. Heinz_, Sep 09 2011