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%I #20 Feb 11 2024 04:44:03
%S 182,24114818,3195165155182,423352992707189818,
%T 56093424824522071350182,7432266601976172417049224818,
%U 984760460172545468089666118585182,130478791444509662828968408963250219818,17288178907829880845340110782723061506860182
%N x-values in the solution to the Pell equation x^2 - 53*y^2 = -1.
%C All terms are multiples of 182.
%H Vincenzo Librandi, <a href="/A228535/b228535.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 (132498,-1).
%F a(n) = 132498*a(n-1)-a(n-2).
%F G.f.: 182*x*(x+1) / (x^2-132498*x+1).
%t CoefficientList[Series[182 (x + 1) / (x^2 - 132498 x + 1), {x, 0, 10}], x] (* _Vincenzo Librandi_, Aug 25 2013 *)
%t LinearRecurrence[{132498,-1},{182,24114818},20] (* _Harvey P. Dale_, Nov 07 2022 *)
%o (PARI) Vec(182*x*(x+1)/(x^2-132498*x+1) + O(x^50))
%Y Cf. A228536 gives the corresponding y-values.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Aug 24 2013