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%I #23 Sep 08 2022 08:45:42
%S 2135,44608,141531,292904,498727,759000,1073723,1442896,1866519,
%T 2344592,2877115,3464088,4105511,4801384,5551707,6356480,7215703,
%U 8129376,9097499,10120072,11197095,12328568,13514491,14754864,16049687,17398960
%N 27225n^2 - 39202n + 14112.
%C The identity (1482401250*n^2-2134548900*n+768398401)^2-(27225*n^2-39202*n+14112) *(8984250*n-6468330)^2=1 can be written as A157770(n)^2-a(n)*A157769(n)^2=1.
%H Vincenzo Librandi, <a href="/A157768/b157768.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*(-2135-38203*x-14112*x^2)/(x-1)^3.
%t Table[27225n^2-39202n+14112,{n,50}] (* _Harvey P. Dale_, Mar 26 2011 *)
%o (Magma) I:=[2135, 44608, 141531]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..30]];
%o (PARI) a(n) = 27225*n^2 - 39202*n + 14112
%Y Cf. A157769, A157770.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 06 2009
%E Entries checked by David Wasserman, Jun 17 2010