|
%I #24 Sep 08 2022 08:45:42
%S 243,485,727,969,1211,1453,1695,1937,2179,2421,2663,2905,3147,3389,
%T 3631,3873,4115,4357,4599,4841,5083,5325,5567,5809,6051,6293,6535,
%U 6777,7019,7261,7503,7745,7987,8229,8471,8713,8955,9197,9439,9681,9923,10165
%N a(n) = 242*n + 1.
%C The identity (242*n + 1)^2 - (121*n^2 + n)*22^2 = 1 can be written as a(n)^2 - A173267(n)*22^2 = 1. - _Vincenzo Librandi_, Feb 06 2012
%H Vincenzo Librandi, <a href="/A157958/b157958.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*(11^2*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*(243-x)/(1-x)^2. - _Vincenzo Librandi_, Feb 06 2012
%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 06 2012
%t LinearRecurrence[{2, -1}, {243, 485}, 50] (* _Vincenzo Librandi_, Feb 06 2012 *)
%t 242*Range[50]+1 (* _Harvey P. Dale_, Sep 01 2015 *)
%o (Magma) I:=[243, 485]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 06 2012
%o (PARI) for(n=1, 40, print1(242*n + 1", ")); \\ _Vincenzo Librandi_, Feb 06 2012
%Y Cf. A173267.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 10 2009
|
