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A157839 1728000n - 1451760. 3

%I

%S 276240,2004240,3732240,5460240,7188240,8916240,10644240,12372240,

%T 14100240,15828240,17556240,19284240,21012240,22740240,24468240,

%U 26196240,27924240,29652240,31380240,33108240,34836240,36564240

%N 1728000n - 1451760.

%C The identity (103680000*n^2-174211200*n+73180801)^2-(3600*n^2-6049*n+2541)*(1728000*n-1451760)^2=1 can be written as A157840(n)^2-A157838(n)*a(n)^2=1.

%H Vincenzo Librandi, <a href="/A157839/b157839.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;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*(276240+1451760*x)/(x-1)^2.

%t LinearRecurrence[{2,-1},{276240,2004240},40]

%o (MAGMA) I:=[276240, 2004240]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

%o (PARI) a(n) = 1728000*n - 1451760.

%Y Cf. A157838, A157840.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 07 2009

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Last modified January 27 05:41 EST 2021. Contains 340455 sequences. (Running on oeis4.)