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%I #21 Sep 08 2022 08:45:42
%S 4801,19601,44401,79201,124001,178801,243601,318401,403201,498001,
%T 602801,717601,842401,977201,1122001,1276801,1441601,1616401,1801201,
%U 1996001,2200801,2415601,2640401,2875201,3120001,3374801,3639601
%N a(n) = 5000*n^2 - 200*n + 1.
%C The identity (5000*n^2 - 200*n + 1)^2 - (25*n^2 - n)*(1000*n - 20)^2 = 1 can be written as a(n)^2 - A157514(n)*A157515(n)^2 = 1 (see also the second part of the comment at A157514). - _Vincenzo Librandi_, Jan 26 2012
%H Vincenzo Librandi, <a href="/A157516/b157516.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5771301&tstart=0">X^2-AY^2=1</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jan 26 2012
%F G.f.: x*(-4801 - 5198*x - x^2)/(x-1)^3. - _Vincenzo Librandi_, Jan 26 2012
%t LinearRecurrence[{3,-3,1},{4801,19601,44401},50] (* _Vincenzo Librandi_, Jan 26 2012 *)
%o (Magma) I:=[4801, 19601, 44401]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Jan 26 2012
%o (PARI) for(n=1, 22, print1(5000*n^2 - 200*n + 1", ")); \\ _Vincenzo Librandi_, Jan 26 2012
%Y Cf. A157514, A157515.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 02 2009
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