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A157956 a(n) = 200*n + 1.

%I A157956 #33 Oct 05 2024 21:06:37
%S A157956 201,401,601,801,1001,1201,1401,1601,1801,2001,2201,2401,2601,2801,
%T A157956 3001,3201,3401,3601,3801,4001,4201,4401,4601,4801,5001,5201,5401,
%U A157956 5601,5801,6001,6201,6401,6601,6801,7001,7201,7401,7601,7801,8001,8201,8401,8601
%N A157956 a(n) = 200*n + 1.
%C A157956 The identity (200*n + 1)^2 - (100*n^2 + n)*20^2 = 1 can be written as a(n)^2 - A055438(n)*20^2 = 1. - _Vincenzo Librandi_, Feb 04 2012
%H A157956 Vincenzo Librandi, <a href="/A157956/b157956.txt">Table of n, a(n) for n = 1..10000</a>
%H A157956 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;tstart=0">X^2-AY^2=1</a>
%H A157956 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*(10^2*t+1)).
%H A157956 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A157956 G.f.: x*(201-x)/(1-x)^2. - _Vincenzo Librandi_, Feb 04 2012
%F A157956 a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 04 2012
%t A157956 200Range[50]+1  (* _Harvey P. Dale_, Feb 24 2011 *)
%t A157956 LinearRecurrence[{2, -1}, {201, 401}, 50] (* _Vincenzo Librandi_, Feb 04 2012 *)
%o A157956 (Magma) I:=[201, 401]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 04 2012
%o A157956 (PARI) for(n=1, 50, print1(200*n + 1", ")); \\ _Vincenzo Librandi_, Feb 04 2012
%Y A157956 Cf. A055438.
%K A157956 nonn,easy
%O A157956 1,1
%A A157956 _Vincenzo Librandi_, Mar 10 2009