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%I #21 Sep 08 2022 08:45:42
%S 442,883,1324,1765,2206,2647,3088,3529,3970,4411,4852,5293,5734,6175,
%T 6616,7057,7498,7939,8380,8821,9262,9703,10144,10585,11026,11467,
%U 11908,12349,12790,13231,13672,14113,14554,14995,15436,15877,16318,16759
%N a(n) = 441*n + 1.
%C The identity (441*n + 1)^2 - (441*n^2 + 2*n)*21^2 = 1 can be written as a(n)^2 - A158321(n)*21^2 = 1. - _Vincenzo Librandi_, Jan 24 2012
%H Vincenzo Librandi, <a href="/A158322/b158322.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 15 in the first table at p. 85, case d(t) = t*(21^2*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*(442-x)/(1-x)^2. - _Vincenzo Librandi_, Jan 24 2012
%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jan 24 2012
%t LinearRecurrence[{2,-1},{442,883},50] (* _Vincenzo Librandi_, Jan 24 2012 *)
%o (Magma) I:=[442, 883]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) for(n=1, 38, print1(441*n+1", ")); \\ _Vincenzo Librandi_, Jan 24 2012
%Y Cf. A158321.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 16 2009