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A157881 Expansion of 152*x^2 / (-x^3+1443*x^2-1443*x+1).

%I A157881 #13 Jul 18 2019 17:27:33
%S A157881 0,152,219336,316282512,456079163120,657665836936680,
%T A157881 948353680783529592,1367525350024012735136,1971970606380945580536672,
%U A157881 2843580246875973503121146040,4100440744024547410555112053160,5912832709303150490046968459510832
%N A157881 Expansion of 152*x^2 / (-x^3+1443*x^2-1443*x+1).
%C A157881 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 A157881     A    * c(n)+1 = a(n)^2,
%C A157881    (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
%C A157881 A157881 is the c(n) sequence for A=9.
%H A157881 Colin Barker, <a href="/A157881/b157881.txt">Table of n, a(n) for n = 1..300</a>
%H A157881 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1443,-1443,1).
%F A157881 G.f.: 152*x^2/(-x^3+1443*x^2-1443*x+1).
%F A157881 c(1) = 0, c(2) = 152, c(3) = 1443*c(2), c(n) = 1443 * (c(n-1)-c(n-2)) + c(n-3) for n>3.
%F A157881 a(n) = -((721+228*sqrt(10))^(-n)*(-1+(721+228*sqrt(10))^n)*(19+6*sqrt(10)+(-19+6*sqrt(10))*(721+228*sqrt(10))^n))/360. - _Colin Barker_, Jul 25 2016
%t A157881 LinearRecurrence[{1443,-1443,1},{0,152,219336},20] (* _Harvey P. Dale_, Jul 18 2019 *)
%o A157881 (PARI) concat(0, Vec(152*x^2/(-x^3+1443*x^2-1443*x+1) + O(x^20))) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A157881 (PARI) a(n) = round(-((721+228*sqrt(10))^(-n)*(-1+(721+228*sqrt(10))^n)*(19+6*sqrt(10)+(-19+6*sqrt(10))*(721+228*sqrt(10))^n))/360) \\ _Colin Barker_, Jul 25 2016
%Y A157881 8*A157881(n)+1 = A097315(n-1)^2.
%Y A157881 9*A157881(n)+1 = A097314(n-1)^2.
%K A157881 nonn,easy
%O A157881 1,2
%A A157881 _Paul Weisenhorn_, Mar 08 2009, Jun 25 2009
%E A157881 Edited by _Alois P. Heinz_, Sep 09 2011