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%I #17 Jan 03 2024 23:45:28
%S 53,1786683,60229083877,2030322415706987,68442168573253447893,
%T 2307185500574051312766043,77775223155909101180089861637,
%U 2621802770278510300206777923017227,88380971308313359064061382604820860533
%N Numbers Y such that 129*Y^2+43 is a square.
%H Vincenzo Librandi, <a href="/A145332/b145332.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 (33710,-1).
%F a(n+2) = 33710*a(n+1)-a(n).
%F G.f.: 53*x*(x+1) / (x^2-33710*x+1). - _Colin Barker_, Oct 21 2014
%e a(1)=53 because the first relation is : 602^2=129*53^2+43.
%t LinearRecurrence[{33710,-1},{53,1786683},20] (* _Harvey P. Dale_, Jan 21 2014 *)
%t CoefficientList[Series[53 (x + 1)/(x^2 - 33710 x + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 21 2014 *)
%o (PARI) Vec(53*x*(x+1)/(x^2-33710*x+1) + O(x^20)) \\ _Colin Barker_, Oct 21 2014
%o (Magma) I:=[53,1786683]; [n le 2 select I[n] else 33710*Self(n-1)-Self(n-2): n in [1..10]]; // _Vincenzo Librandi_, Oct 21 2014
%K easy,nonn
%O 1,1
%A _Richard Choulet_, Oct 08 2008
%E Editing from _Colin Barker_, Oct 21 2014
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