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%I #23 Sep 08 2022 08:45:42
%S 99,3480,11663,24648,42435,65024,92415,124608,161603,203400,249999,
%T 301400,357603,418608,484415,555024,630435,710648,795663,885480,
%U 980099,1079520,1183743,1292768,1406595,1525224,1648655,1776888,1909923
%N a(n) = 2401*n^2 - 3822*n + 1520.
%C The identity (2401*n^2-3822*n+1520)^2-(49*n^2-78*n+31)*( 343*n-273)^2=1 can be written as a(n)^2-A157368(n)*A157369(n)^2=1.
%H Vincenzo Librandi, <a href="/A157370/b157370.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773147&tstart=0">X^2-AY^2=1</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(1)=99, a(2)=3480, a(3)=11663, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Dec 03 2011]
%F G.f.: x*(1520*x^2 + 3183*x + 99)/(1-x)^3. - _Harvey P. Dale_, Dec 03 2011
%F E.g.f.: (1520 - 1421*x + 2401*x^2)*exp(x) - 1520. - _G. C. Greubel_, Feb 02 2018
%t Table[2401n^2-3822n+1520,{n,40}] (* or *) LinearRecurrence[{3,-3,1},{99,3480,11663},40] (* _Harvey P. Dale_, Dec 03 2011 *)
%o (Magma) I:=[99, 3480, 11663]; [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)=2401*n^2-3822*n+1520 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A157368, A157369.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 28 2009
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