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%I #15 Sep 08 2022 08:45:42
%S 403201,117014401,440985601,972316801,1711008001,2657059201,
%T 3810470401,5171241601,6739372801,8514864001,10497715201,12687926401,
%U 15085497601,17690428801,20502720001,23522371201,26749382401,30183753601
%N 103680000n^2 - 194428800n + 91152001.
%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 a(n)^2-A157824(n)*A157825(n)^2=1.
%H Vincenzo Librandi, <a href="/A157826/b157826.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*(-403201-115804798*x-91152001*x^2)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{403201,117014401,440985601},40]
%o (Magma) I:=[403201, 117014401, 440985601]; [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) = 103680000*n^2 - 194428800*n + 91152001.
%Y Cf. A157824, A157825.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 07 2009
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