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%I #27 Sep 08 2022 08:45:42
%S 167,672,1515,2696,4215,6072,8267,10800,13671,16880,20427,24312,28535,
%T 33096,37995,43232,48807,54720,60971,67560,74487,81752,89355,97296,
%U 105575,114192,123147,132440,142071,152040,162347,172992,183975,195296
%N 169n^2 - 2n.
%C The identity (169*n-1)^2-(169*n^2-2*n)*(13)^2=1 can be written as A158219(n)^2-a(n)*(13)^2=1.
%H Vincenzo Librandi, <a href="/A158218/b158218.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_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%F G.f.: x*(-167-171*x)/(x-1)^3.
%t LinearRecurrence[{3,-3,1},{167,672,1515},50]
%o (Magma) I:=[167, 672, 1515]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
%o (PARI) a(n) = 169*n^2 - 2*n.
%Y Cf. A158219.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 14 2009
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