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A174757 x-values in the solution to x^2-53*y^2=1. 2

%I #10 Sep 08 2022 08:45:51

%S 1,66249,8777860001,1163048894346249,154101652394311440001,

%T 20418160737778428282906249,2705365461280064538234200740001,

%U 358455512868267830449176701365746249

%N x-values in the solution to x^2-53*y^2=1.

%C The corresponding values of y of this Pell equation are in A174983.

%H Vincenzo Librandi, <a href="/A174757/b174757.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (132498,-1).

%F a(n) = 132498*a(n-1)-a(n-2) with a(1)=1, a(2)=66249.

%F G.f.: x*(1-66249*x)/(1-132498*x+x^2)

%t LinearRecurrence[{132498,-1},{1,66249},30]

%o (Magma) I:=[1, 66249]; [n le 2 select I[n] else 132498*Self(n-1)-Self(n-2): n in [1..20]];

%Y Cf. A174983.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Apr 13 2010

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