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%I #22 Sep 08 2022 08:45:42
%S 1728240,3456240,5184240,6912240,8640240,10368240,12096240,13824240,
%T 15552240,17280240,19008240,20736240,22464240,24192240,25920240,
%U 27648240,29376240,31104240,32832240,34560240,36288240,38016240
%N a(n) = 1728000*n + 240.
%C The identity (103680000*n^2 + 28800*n + 1)^2 - (3600*n^2 + n)*(1728000*n + 240)^2 = 1 can be written as A157863(n)^2 - A157861(n)*a(n)^2 = 1. - _Vincenzo Librandi_, Jan 25 2012
%H Vincenzo Librandi, <a href="/A157862/b157862.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 G.f.: x*(1728240 - 240*x)/(1-x)^2. - _Colin Barker_, Jan 17 2012
%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jan 25 2012
%t LinearRecurrence[{2,-1},{1728240,3456240},40] (* _Vincenzo Librandi_, Jan 25 2012 *)
%o (Magma) I:=[1728240, 3456240]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jan 25 2012
%o (PARI) for(n=1, 22, print1(1728000*n + 240", ")); \\ _Vincenzo Librandi_, Jan 25 2012
%Y Cf. A157861, A157863.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 08 2009
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