A158330 - OEIS

%I #17 Sep 08 2022 08:45:42

%S 483,967,1451,1935,2419,2903,3387,3871,4355,4839,5323,5807,6291,6775,

%T 7259,7743,8227,8711,9195,9679,10163,10647,11131,11615,12099,12583,

%U 13067,13551,14035,14519,15003,15487,15971,16455,16939,17423,17907

%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-A158329(n)*(22)^2=1.

%H Vincenzo Librandi, <a href="/A158330/b158330.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 a(n) = 2*a(n-1)-a(n-2).

%F G.f.: x*(483+x)/(1-x)^2.

%t LinearRecurrence[{2,-1},{483,967},50]

%o (Magma) I:=[483, 967]; [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. A158329.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 16 2009