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%I #12 Sep 08 2022 08:45:42
%S 66249,1302499,4101249,8462499,14386249,21872499,30921249,41532499,
%T 53706249,67442499,82741249,99602499,118026249,138012499,159561249,
%U 182672499,207346249,233582499,261381249,290742499,321666249,354152499
%N 781250n^2 - 1107500n + 392499.
%C The identity (781250*n^2-1107500*n+392499)^2-(625*n^2-886*n +314)*(31250*n-22150)^2=1 can be written as a(n)^2-A157618(n)*A157619(n)^2=1.
%H Vincenzo Librandi, <a href="/A157620/b157620.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773864&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*(-66249-1103752*x-392499*x^2)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{66249,1302499,4101249},30]
%o (Magma) I:=[66249, 1302499, 4101249]; [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) = 781250*n^2 - 1107500*n + 392499.
%Y Cf. A157618, A157619.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 03 2009
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