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 A175015 y-values in the solution to x^2-57*y^2=1. 2

%I #32 Oct 11 2023 15:19:05

%S 0,20,6040,1824060,550860080,166357920100,50239541010120,

%T 15172175027136140,4581946618654104160,1383732706658512320180,

%U 417882695464252066590200,126199190297497465597920220

%N y-values in the solution to x^2-57*y^2=1.

%C The corresponding values of x of this Pell equation are in A174759.

%H Vincenzo Librandi, <a href="/A175015/b175015.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 (302,-1).

%F a(n) = 302*a(n-1)-a(n-2) with a(1)=0, a(2)=20.

%F G.f.: 20*x^2/(1-302*x+x^2).

%F a(n) = ((151+20*sqrt(57))^(n-1) - (151-20*sqrt(57))^(n-1)) / (2*sqrt(57)). - _Alan Michael Gómez Calderón_, Oct 06 2023

%t LinearRecurrence[{302,-1},{0,20},30]

%o (Magma) I:=[0, 20]; [n le 2 select I[n] else 302*Self(n-1)-Self(n-2): n in [1..20]];

%Y Cf. A174759.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Apr 15 2010

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Last modified July 22 23:01 EDT 2024. Contains 374544 sequences. (Running on oeis4.)