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%I #21 Sep 08 2022 08:45:42
%S 168,337,506,675,844,1013,1182,1351,1520,1689,1858,2027,2196,2365,
%T 2534,2703,2872,3041,3210,3379,3548,3717,3886,4055,4224,4393,4562,
%U 4731,4900,5069,5238,5407,5576,5745,5914,6083,6252,6421,6590,6759,6928,7097,7266
%N 169n - 1.
%C The identity (169*n-1)^2-(1169*n^2-2*n)*(13)^2=1 can be written as a(n)^2-A158218(n)*(13)^2=1.
%H Vincenzo Librandi, <a href="/A158219/b158219.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*(13^2*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*(168+x)/(1-x)^2.
%t LinearRecurrence[{2,-1},{168,337},50]
%t 169*Range[50]-1 (* _Harvey P. Dale_, Mar 17 2018 *)
%o (Magma) I:=[168, 337]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n) = 169*n - 1.
%Y Cf. A158218.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 14 2009
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