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

0, 4, 120, 3596, 107760, 3229204, 96768360, 2899821596, 86897879520, 2604036564004, 78034199040600, 2338421934653996, 70074623840579280, 2099900293282724404, 62926934174641152840, 1885708124945951860796

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Tanya Khovanova, Recursive Sequences

H. W. Lenstra Jr., Solving the Pell Equation, Notices of the AMS, Vol.49, No.2, Feb. 2002, p.182-192.

Index entries for linear recurrences with constant coefficients, signature (30,-1).

Formula

x_n + y_n*sqrt(14) = (x_1 + y_1*sqrt(14))^n.

From Vladeta Jovovic, Mar 25 2002: (Start)

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)).

Recurrence: a(n) = 30*a(n-1)-a(n-2).

G.f.: 4*x/(1-30*x+x^2). (End)

Maple

Digits := 1000: q := seq(floor(evalf(((15+4*sqrt(14))^n-(15-4*sqrt(14))^n)/28*sqrt(14))+0.1), n=1..30);

Mathematica

LinearRecurrence[{30, -1}, {0, 4}, 16] (* Ray Chandler, Aug 11 2015 *)

Crossrefs

Cf. A068203.

Sequence in context: A240397 A347425 A002702 * A203033 A307935 A001332

Adjacent sequences: A068201 A068202 A068203 * A068205 A068206 A068207

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 24 2002

Extensions

More terms from Sascha Kurz, Mar 25 2002

More terms from Vladeta Jovovic, Mar 25 2002

Initial term 0 added by N. J. A. Sloane, Jul 05 2010

Status

approved