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A158326 484n + 1. 2

%I

%S 485,969,1453,1937,2421,2905,3389,3873,4357,4841,5325,5809,6293,6777,

%T 7261,7745,8229,8713,9197,9681,10165,10649,11133,11617,12101,12585,

%U 13069,13553,14037,14521,15005,15489,15973,16457,16941,17425,17909

%N 484n + 1.

%C The identity (484*n+1)^2-(484*n^2+2*n)*(22)^2=1 can be written as a(n)^2-A158325(n)*(22)^2=1.

%H Vincenzo Librandi, <a href="/A158326/b158326.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*(22^2*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*(485-x)/(1-x)^2.

%F a(n) = 2*a(n-1)-a(n-2).

%t LinearRecurrence[{2,-1},{485,969},50]

%t 484*Range[40]+1 (* _Harvey P. Dale_, Apr 29 2018 *)

%o (MAGMA) I:=[485, 969]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

%o (PARI) a(n) = 484*n + 1.

%Y Cf. A158325.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 16 2009

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Last modified June 1 09:53 EDT 2020. Contains 334762 sequences. (Running on oeis4.)