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%I #24 Sep 08 2022 08:45:42
%S 1440,2898,4356,5814,7272,8730,10188,11646,13104,14562,16020,17478,
%T 18936,20394,21852,23310,24768,26226,27684,29142,30600,32058,33516,
%U 34974,36432,37890,39348,40806,42264,43722,45180,46638,48096,49554
%N a(n) = 1458*n - 18.
%C The identity (13122*n^2 - 324*n + 1)^2 - (81*n^2 - 2*n)*(1458*n - 18)^2 = 1 can be written as A157509(n)^2 - A157507(n)*a(n)^2 = 1 (see also second comment at A157509). - _Vincenzo Librandi_, Jan 26 2012
%H Vincenzo Librandi, <a href="/A157508/b157508.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5771301&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). - _Vincenzo Librandi_, Jan 26 2012
%F G.f.: 18*(82*x-1)/(x-1)^2. - _Vincenzo Librandi_, Jan 26 2012 [corrected by _Georg Fischer_, May 11 2019]
%t LinearRecurrence[{2,-1},{1440,2898},40] (* _Vincenzo Librandi_, Jan 26 2012 *)
%o (Magma) I:=[1440, 2898]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Jan 26 2012
%o (PARI) for(n=1, 35, print1(1458*n - 18", ")); \\ _Vincenzo Librandi_, Jan 26 2012
%Y Cf. A157507, A157509.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 02 2009
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