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%I #14 Sep 08 2022 08:45:42
%S 768398401,4385348551,10967101201,20513656351,33025014001,48501174151,
%T 66942136801,88347901951,112718469601,140053839751,170354012401,
%U 203618987551,239848765201,279043345351,321202728001,366326913151,414415900801
%N 1482401250n^2 - 830253600n + 116250751.
%C The identity (1482401250*n^2-830253600*n +116250751)^2-(27225*n^2-15248*n +2135) *(8984250*n -2515920)^2=1 can be written as a(n)^2-A157786(n)*A157787(n)^2=1.
%H Vincenzo Librandi, <a href="/A157788/b157788.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&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).
%F G.f: x*(-768398401-2080153348*x-116250751*x^2)/(x-1)^3.
%t Table[1482401250n^2-830253600n+116250751,{n,30}]
%o (Magma) I:=[768398401, 4385348551, 10967101201]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..30]];
%o (PARI) a(n) = 1482401250*n^2 - 830253600*n + 116250751.
%Y Cf. A157786, A157787.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 06 2009
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