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 A157730 441n^2 - 488n + 135. 3

%I

%S 88,923,2640,5239,8720,13083,18328,24455,31464,39355,48128,57783,

%T 68320,79739,92040,105223,119288,134235,150064,166775,184368,202843,

%U 222200,242439,263560,285563,308448,332215,356864,382395,408808,436103,464280

%N 441n^2 - 488n + 135.

%C The identity(388962*n^2-430416*n+119071)^2-(441*n^2-488*n+135)*(18522*n-10248)^2=1 can be written as A157732(n)^2-a(n)*A157731(n)^2=1.

%H Vincenzo Librandi, <a href="/A157730/b157730.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773864&amp;tstart=0">X^2-AY^2=1</a>

%H <a href="/Sindx_Rea.html#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

%F G.f.: x*(-88-659*x-135*x^2)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{88,923,2640},40]

%o (MAGMA) I:=[88, 923, 2640]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

%o (PARI) a(n) = 441*n^2 - 488*n + 135.

%Y Cf. 157731, A157732.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 05 2009

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