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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}. 2
0, 4, 120, 3596, 107760, 3229204, 96768360, 2899821596, 86897879520, 2604036564004, 78034199040600, 2338421934653996, 70074623840579280, 2099900293282724404, 62926934174641152840, 1885708124945951860796 (list; graph; refs; listen; history; text; internal format)
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.

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). - Vladeta Jovovic, Mar 25 2002

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: A006434 A240397 A002702 * A203033 A001332 A071304

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

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Last modified July 28 12:53 EDT 2017. Contains 289889 sequences.