A158221 - OEIS

%I #22 Sep 08 2022 08:45:42

%S 170,339,508,677,846,1015,1184,1353,1522,1691,1860,2029,2198,2367,

%T 2536,2705,2874,3043,3212,3381,3550,3719,3888,4057,4226,4395,4564,

%U 4733,4902,5071,5240,5409,5578,5747,5916,6085,6254,6423,6592,6761,6930,7099,7268

%N a(n) = 169n + 1.

%C The identity (169*n+1)^2 - (169*n^2 + 2*n)*(13)^2 = 1 can be written as a(n)^2 - A158220(n)*(13)^2 = 1. - _Vincenzo Librandi_, Feb 02 2012

%H Vincenzo Librandi, <a href="/A158221/b158221.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;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 G.f.: x*(170-x)/(1-x)^2. - _Vincenzo Librandi_, Feb 02 2012

%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 02 2012

%t LinearRecurrence[{2, -1}, {170, 339}, 50] (* _Vincenzo Librandi_, Feb 02 2012 *)

%o (PARI) a(n)=169*n+1 \\ _Charles R Greathouse IV_, Dec 28 2011

%o (Magma) I:=[170, 339]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 02 2012

%Y Cf. A158220.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 14 2009