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%I #22 Sep 08 2022 08:45:43
%S 899,1799,2699,3599,4499,5399,6299,7199,8099,8999,9899,10799,11699,
%T 12599,13499,14399,15299,16199,17099,17999,18899,19799,20699,21599,
%U 22499,23399,24299,25199,26099,26999,27899,28799,29699,30599,31499
%N a(n) = 900*n - 1.
%C The identity (900*n - 1)^2 - (900*n^2 - 2*n)*30^2=1 can be written as a(n)^2 - A158408(n)*30^2 = 1.
%H Vincenzo Librandi, <a href="/A158409/b158409.txt">Table of n, a(n) for n = 1..10000</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*(30^2*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); a(1)=899, a(2)=1799. - _Harvey P. Dale_, Dec 08 2011
%F G.f.: x*(899+x)/(x-1)^2. - _Bruno Berselli_, Dec 08 2011
%t 900*Range[40]-1 (* or *) LinearRecurrence[{2,-1},{899,1799},40] (* _Harvey P. Dale_, Dec 08 2011 *)
%o (Magma) I:=[899,1799]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 12 2012
%o (PARI) for(n=1, 50, print1(900*n - 1", ")); \\ _Vincenzo Librandi_, Feb 12 2012
%Y Cf. A158408.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 18 2009
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