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%I #14 Jan 03 2024 23:46:06
%S 14,1526,167846,18461534,2030600894,223347636806,24566209447766,
%T 2702059691617454,297201999868472174,32689517925840321686,
%U 3595549769842566913286,395477785164756520139774,43498960818353374648461854,4784490212233706454810664166
%N Numbers X such that there exists Y in N with X^2=21*Y^2+7.
%H Vincenzo Librandi, <a href="/A145693/b145693.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 (110,-1).
%F a(n+2) = 110*a(n+1)-a(n).
%F G.f.: -14*x*(x-1) / (x^2-110*x+1). - _Colin Barker_, Oct 21 2014
%e a(1)=14 because the first relation is 14^2=21*3^2+7.
%t CoefficientList[Series[14 (1 - x)/(x^2 - 110 x + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 21 2014 *)
%o (PARI) Vec(-14*x*(x-1)/(x^2-110*x+1) + O(x^20)) \\ _Colin Barker_, Oct 21 2014
%o (Magma) I:=[14,1526]; [n le 2 select I[n] else 110*Self(n-1)-Self(n-2): n in [1..15]]; // _Vincenzo Librandi_, Oct 21 2014
%Y Cf. A144927, A144928, A144929, A144930.
%K easy,nonn
%O 1,1
%A _Richard Choulet_, Oct 16 2008
%E Editing and more terms from _Colin Barker_, Oct 21 2014
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