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%I #15 Jan 03 2024 23:46:17
%S 7,4137,2440823,1440081433,849645604647,501289466660297,
%T 295759935683970583,174497860764075983673,102953442090869146396487,
%U 60742356335752032297943657,35837887284651608186640361143,21144292755588113078085515130713
%N Numbers Y such that 111*Y^2+37 is a square.
%H Vincenzo Librandi, <a href="/A145696/b145696.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 (590,-1).
%F a(n+2) = 590*a(n+1)-a(n).
%F G.f.: 7*x*(x+1) / (x^2-590*x+1). - _Colin Barker_, Oct 21 2014
%e a(1)=7 because the first relation is 74^2=111*7^2+37.
%t CoefficientList[Series[7 (x + 1)/(x^2 - 590 x + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 21 2014 *)
%o (PARI) Vec(7*x*(x+1)/(x^2-590*x+1) + O(x^20)) \\ _Colin Barker_, Oct 21 2014
%o (Magma) I:=[7,4137]; [n le 2 select I[n] else 590*Self(n-1)-Self(n-2): n in [1..15]]; // _Vincenzo Librandi_, Oct 21 2014
%K easy,nonn
%O 1,1
%A _Richard Choulet_, Oct 16 2008
%E Editing and more terms from _Colin Barker_, Oct 21 2014