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y-values in the solution to x^2-70*y^2=1.
2

%I #25 Mar 20 2023 13:46:16

%S 0,30,15060,7560090,3795150120,1905157800150,956385420525180,

%T 480103575945840210,241011038739391260240,120987061343598466800270,

%U 60735263783447690942475300,30488981432229397254655800330

%N y-values in the solution to x^2-70*y^2=1.

%C The corresponding values of x of this Pell equation are in A176377.

%H Vincenzo Librandi, <a href="/A176378/b176378.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 (502,-1).

%F a(n) = 502*a(n-1)-a(n-2) with a(1)=0, a(2)=30.

%F G.f.: 30*x^2/(1-502*x+x^2).

%F a(n) = ((25+3r)^(2n-2)-(25-3r)^(2n-2))/(2r*5^(n-1)), where r=sqrt(70). - _Bruno Berselli_, Dec 14 2011

%t LinearRecurrence[{502,-1},{0,30},20]

%o (Magma) I:=[0,30]; [n le 2 select I[n] else 502*Self(n-1)-Self(n-2): n in [1..20]];

%o (Maxima) makelist(expand(((25+3*sqrt(70))^(2*n-2)-(25-3*sqrt(70))^(2*n-2))/(2*sqrt(70)*5^(n-1))), n, 1, 12); /* _Bruno Berselli_, Dec 14 2011 */

%Y Cf. A176377.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Apr 16 2010