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A157854 1728000n - 384240. 3

%I

%S 1343760,3071760,4799760,6527760,8255760,9983760,11711760,13439760,

%T 15167760,16895760,18623760,20351760,22079760,23807760,25535760,

%U 27263760,28991760,30719760,32447760,34175760,35903760,37631760

%N 1728000n - 384240.

%C The identity (103680000*n^2-46108800*n+5126401)^2-(3600*n^2-1601*n +178)*(1728000*n-384240)^2=1 can be written as A157855(n)^2-A157853(n)*a(n)^2=1.

%H Vincenzo Librandi, <a href="/A157854/b157854.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*(1343760+384240*x)/(x-1)^2.

%t LinearRecurrence[{2,-1},{1343760,3071760},40]

%o (Magma) I:=[1343760, 3071760]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

%o (PARI) a(n) = 1728000*n - 384240.

%Y Cf, A157853, A157855.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 08 2009

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Last modified January 30 02:40 EST 2023. Contains 359939 sequences. (Running on oeis4.)