%I #23 Sep 08 2022 08:45:42
%S 339,677,1015,1353,1691,2029,2367,2705,3043,3381,3719,4057,4395,4733,
%T 5071,5409,5747,6085,6423,6761,7099,7437,7775,8113,8451,8789,9127,
%U 9465,9803,10141,10479,10817,11155,11493,11831,12169,12507,12845,13183,13521
%N a(n) = 338*n + 1.
%C The identity (338*n + 1)^2 - (169*n^2 + n)*26^2 = 1 can be written as a(n)^2 - A173275(n)*26^2 = 1. - _Vincenzo Librandi_, Feb 10 2012
%H Vincenzo Librandi, <a href="/A158000/b158000.txt">Table of n, a(n) for n = 1..10000</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_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: x*(339-x)/(1-x)^2. - _Vincenzo Librandi_, Feb 10 2012
%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 10 2012
%t LinearRecurrence[{2, -1}, {339, 677}, 50] (* _Vincenzo Librandi_, Feb 10 2012 *)
%t 338*Range[50]+1 (* _Harvey P. Dale_, Feb 18 2012 *)
%o (Magma) I:=[339, 677]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 10 2012
%o (PARI) for(n=1, 50, print1(338*n + 1", ")); \\ _Vincenzo Librandi_, Feb 10 2012
%Y Cf. A173275.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 14 2009