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A068204 Let (x_n, y_n) be n-th solution to the Pell equation x^2 = 14*y^2 + 1. Sequence gives {y_n}.

%I A068204 #22 Jun 26 2020 06:05:26
%S A068204 0,4,120,3596,107760,3229204,96768360,2899821596,86897879520,
%T A068204 2604036564004,78034199040600,2338421934653996,70074623840579280,
%U A068204 2099900293282724404,62926934174641152840,1885708124945951860796
%N A068204 Let (x_n, y_n) be n-th solution to the Pell equation x^2 = 14*y^2 + 1. Sequence gives {y_n}.
%H A068204 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A068204 H. W. Lenstra Jr., <a href="http://www.ams.org/notices/200202/fea-lenstra.pdf">Solving the Pell Equation</a>, Notices of the AMS, Vol.49, No.2, Feb. 2002, p.182-192.
%H A068204 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (30,-1).
%F A068204 x_n + y_n*sqrt(14) = (x_1 + y_1*sqrt(14))^n.
%F A068204 From _Vladeta Jovovic_, Mar 25 2002: (Start)
%F A068204 a(n) = (2+15/28*sqrt(14))*(-1/(-15-4*sqrt(14)))^n/(-15-4*sqrt(14))+(-15/28*sqrt(14)+2)*(-1/(-15+4*sqrt(14)))^n/(-15+4*sqrt(14)).
%F A068204 Recurrence: a(n) = 30*a(n-1)-a(n-2).
%F A068204 G.f.: 4*x/(1-30*x+x^2). (End)
%p A068204 Digits := 1000: q := seq(floor(evalf(((15+4*sqrt(14))^n-(15-4*sqrt(14))^n)/28*sqrt(14))+0.1),n=1..30);
%t A068204 LinearRecurrence[{30, -1},{0, 4},16] (* _Ray Chandler_, Aug 11 2015 *)
%Y A068204 Cf. A068203.
%K A068204 nonn,easy
%O A068204 1,2
%A A068204 _N. J. A. Sloane_, Mar 24 2002
%E A068204 More terms from _Sascha Kurz_, Mar 25 2002
%E A068204 More terms from _Vladeta Jovovic_, Mar 25 2002
%E A068204 Initial term 0 added by _N. J. A. Sloane_, Jul 05 2010