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x-values in the solution to x^2-31*y^2=1.
2

%I #13 Sep 08 2022 08:45:51

%S 1,1520,4620799,14047227440,42703566796801,129818829015047600,

%T 394649197502177907199,1199733430587791822837360,

%U 3647189234337689639247667201,11087454072653145915521085453680

%N x-values in the solution to x^2-31*y^2=1.

%C The corresponding values of y of this Pell equation are in A174771.

%H Vincenzo Librandi, <a href="/A174746/b174746.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 (3040,-1).

%F a(n) = 3040*a(n-1)-a(n-2) with a(1)=1, a(2)=1520.

%F G.f.: x*(1-1520*x)/(1-3040*x+x^2).

%t LinearRecurrence[{3040,-1},{1,1520},30]

%o (Magma) I:=[1, 1520]; [n le 2 select I[n] else 3040*Self(n-1)-Self(n-2): n in [1..20]];

%Y Cf. A174771.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Apr 12 2010