%I #21 Jan 03 2024 23:46:35
%S 254,515366,1046192726,2123770718414,4311253512187694,
%T 8751842505970300406,17766235975866197636486,
%U 36065450279165875231766174,73212846300470750854287696734,148622041924505345068328792603846
%N Numbers X such that there exists Y in N with X^2 = 381*Y^2 + 127.
%H Vincenzo Librandi, <a href="/A145715/b145715.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2030,-1).
%F a(n+2) = 2030*a(n+1) - a(n).
%F G.f.: -254*x*(x-1) / (x^2-2030*x+1). - _Colin Barker_, Oct 21 2014
%e a(1)=254 because the first relation is 254^2=381*13^2+127.
%t LinearRecurrence[{2030,-1},{254,515366},10] (* _Harvey P. Dale_, Dec 21 2011 *)
%t CoefficientList[Series[254 (1 - x)/(x^2 - 2030 x + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 21 2014 *)
%o (PARI) Vec(-254*x*(x-1)/(x^2-2030*x+1) + O(x^20)) \\ _Colin Barker_, Oct 21 2014
%o (Magma) I:=[254,515366]; [n le 2 select I[n] else 2030*Self(n-1)-Self(n-2): n in [1..15]]; // _Vincenzo Librandi_, Oct 21 2014
%K nonn,easy
%O 1,1
%A _Richard Choulet_, Oct 16 2008
%E Edited by _Colin Barker_, Oct 21 2014