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%I #30 Sep 08 2022 08:45:42
%S 1727760,3455760,5183760,6911760,8639760,10367760,12095760,13823760,
%T 15551760,17279760,19007760,20735760,22463760,24191760,25919760,
%U 27647760,29375760,31103760,32831760,34559760,36287760,38015760
%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 A157859(n)^2 - A157857(n)*a(n)^2 = 1. - _Vincenzo Librandi_, Jan 25 2012
%C This is the case s=60 of the identity (8*n^2*s^4 - 8*n*s^2 + 1)^2 - (n^2*s^2 - n)*(8*n*s^3 - 4*s)^2 = 1. - _Bruno Berselli_, Jan 25 2012
%H Vincenzo Librandi, <a href="/A157858/b157858.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*(1727760 + 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},{1727760,3455760},40] (* _Vincenzo Librandi_, Jan 25 2012 *)
%o (Magma) I:=[1727760, 3455760]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Jan 25 2012
%o (PARI) for(n=1, 22, print1(1728000*n - 240", ")); \\ _Vincenzo Librandi_, Jan 25 2012
%Y Cf. A157857, A157859.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 08 2009
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