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%I #24 Sep 08 2022 08:45:42
%S 168,674,1518,2700,4220,6078,8274,10808,13680,16890,20438,24324,28548,
%T 33110,38010,43248,48824,54738,60990,67580,74508,81774,89378,97320,
%U 105600,114218,123174,132468,142100,152070,162378,173024,184008,195330
%N 169n^2 - n.
%C The identity (338*n-1)^2-(169*n^2-n)*(26)^2=1 can be written as A157999(n)^2-a(n)*(26)^2=1.
%H Vincenzo Librandi, <a href="/A157998/b157998.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 14 in the first table at p. 85, case d(t) = t*(13^2*t-1)).
%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*(168+170*x)/(1-x)^3. [Colin Barker, Jan 17 2012]
%p A157998:=n->169*n^2 - n; seq(A157998(n), n=1..50); # _Wesley Ivan Hurt_, Jan 30 2014
%t LinearRecurrence[{3,-3,1},{168,674,1518},50]
%o (Magma) I:=[168, 674, 1518]; [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 - n.
%Y Cf. A157999.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 11 2009
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