%I #19 Sep 08 2022 08:45:42
%S 1520,7743,18768,34595,55224,80655,110888,145923,185760,230399,279840,
%T 334083,393128,456975,525624,599075,677328,760383,848240,940899,
%U 1038360,1140623,1247688,1359555,1476224,1597695,1723968,1855043,1990920
%N a(n) = 2401*n^2 - 980*n + 99.
%C The identity (2401*n^2-980*n+99)^2-(49*n^2-20*n +2)*(343*n-70)^2=1 can be written as a(n)^2-A157373(n)*A157374(n)^2=1. - _Vincenzo Librandi_, Jan 28 2012
%H Vincenzo Librandi, <a href="/A157375/b157375.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(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Vincenzo Librandi_, Jan 28 2012
%F G.f.: x*(-1520-3183*x-99*x^2)/(x-1)^3. - _Vincenzo Librandi_, Jan 28 2012
%F E.g.f.: (49*x*(49*x + 29) + 99)*exp(x) - 99. - _G. C. Greubel_, Feb 04 2018
%t LinearRecurrence[{3,-3,1},{1520,7743,18768},40] (* _Vincenzo Librandi_, Jan 28 2012 *)
%t Table[2401*n^2 - 980*n + 99, {n,1,30}] (* _G. C. Greubel_, Feb 04 2018 *)
%t CoefficientList[Series[(-1520-3183x-99x^2)/(-1+x)^3,{x,0,40}],x] (* _Harvey P. Dale_, Jul 27 2021 *)
%o (Magma) I:=[1520, 7743, 18768]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Jan 28 2012
%o (PARI) for(n=1, 40, print1(2401*n^2 - 980*n + 99", ")); \\ _Vincenzo Librandi_, Jan 28 2012
%Y Cf. A157373, A157374.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 28 2009