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%I #18 Sep 08 2022 08:45:42
%S 9100,40350,71600,102850,134100,165350,196600,227850,259100,290350,
%T 321600,352850,384100,415350,446600,477850,509100,540350,571600,
%U 602850,634100,665350,696600,727850,759100,790350,821600,852850,884100,915350
%N 31250n - 22150.
%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 A157620(n)^2-A157618(n)*a(n)^2=1.
%H Vincenzo Librandi, <a href="/A157619/b157619.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_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*(9100+22150*x)/(x-1)^2.
%t LinearRecurrence[{2,-1},{9100,40350},30]
%o (Magma) I:=[9100,40350]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
%o (PARI) a(n) = 31250*n - 22150.
%Y Cf. A157618, A157620.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 03 2009
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