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%I #15 Sep 08 2022 08:45:42
%S 325,649,973,1297,1621,1945,2269,2593,2917,3241,3565,3889,4213,4537,
%T 4861,5185,5509,5833,6157,6481,6805,7129,7453,7777,8101,8425,8749,
%U 9073,9397,9721,10045,10369,10693,11017,11341,11665,11989,12313,12637,12961
%N 324n + 1.
%C The identity (324*n+1)^2-(324*n^2+2*n)*(18)^2=1 can be written as a(n)^2-A158271(n)*(18)^2=1.
%H Vincenzo Librandi, <a href="/A158272/b158272.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 E. J. Barbeau, <a href="http://www.math.toronto.edu/barbeau/home.html">Polynomial Excursions</a>, Chapter 10: <a href="http://www.math.toronto.edu/barbeau/hxpol10.pdf">Diophantine equations</a> (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(18^2*t+2)).
%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*(325-x)/(1-x)^2.
%t LinearRecurrence[{2,-1},{325,649},50]
%o (Magma) I:=[325, 649]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n) = 324*n + 1.
%Y Cf. A158271.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 15 2009
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