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%I #13 Sep 08 2022 08:45:42
%S 14,4063,15312,33761,59410,92259,132308,179557,234006,295655,364504,
%T 440553,523802,614251,711900,816749,928798,1048047,1174496,1308145,
%U 1448994,1597043,1752292,1914741,2084390,2261239,2445288,2636537
%N 3600n^2 - 6751n + 3165.
%C The identity (103680000*n^2-194428800*n+91152001)^2-(3600*n^2-6751*n+3165)*(1728000*n-1620240)^2=1 can be written as A157826(n)^2-a(n)*A157825(n)^2=1.
%H Vincenzo Librandi, <a href="/A157824/b157824.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*(-14-4021*x-3165*x^2)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{14,4063,15312},40]
%o (Magma) I:=[14, 4063, 15312]; [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) = 3600*n^2 - 6751*n + 3165.
%Y Cf. A157825, A157826.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 07 2009
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