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%I #18 Sep 08 2022 08:45:42
%S 107760,1835760,3563760,5291760,7019760,8747760,10475760,12203760,
%T 13931760,15659760,17387760,19115760,20843760,22571760,24299760,
%U 26027760,27755760,29483760,31211760,32939760,34667760,36395760
%N 1728000n - 1620240.
%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-A157824(n)*a(n)^2=1.
%H Vincenzo Librandi, <a href="/A157825/b157825.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_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 2*a(n-1) -a(n-2).
%F G.f.: x*(107760+1620240*x)/(x-1)^2.
%t LinearRecurrence[{2,-1},{107760,1835760},40]
%t 1728000Range[50]-1620240 (* _Harvey P. Dale_, Mar 23 2011 *)
%o (Magma) I:=[107760, 1835760]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n) = 1728000*n - 1620240.
%Y Cf. A157824, A157826.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 07 2009
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