%I #21 Sep 08 2022 08:45:42
%S 1476,2934,4392,5850,7308,8766,10224,11682,13140,14598,16056,17514,
%T 18972,20430,21888,23346,24804,26262,27720,29178,30636,32094,33552,
%U 35010,36468,37926,39384,40842,42300,43758,45216,46674,48132,49590
%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 A157506(n)^2 - A177099(n)*a(n)^2 = 1 (see _Bruno Berselli_'s comment at A177099). - _Vincenzo Librandi_, Feb 04 2012
%H Vincenzo Librandi, <a href="/A157505/b157505.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 G.f.: x*(1476 - 18*x)/(1-x)^2. - _Vincenzo Librandi_, Feb 04 2012
%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 04 2012
%t LinearRecurrence[{2, -1}, {1476, 2934}, 50] (* _Vincenzo Librandi_, Feb 04 2012 *)
%t 1458*Range[40]+18 (* _Harvey P. Dale_, Aug 17 2016 *)
%o (Magma) I:=[1476, 2934]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 04 2012
%o (PARI) for(n=1, 40, print1(1458n + 18", ")); \\ _Vincenzo Librandi_, Feb 04 2012
%Y Cf. A157506, A177099.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 02 2009