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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}.
4
0, 4, 120, 3596, 107760, 3229204, 96768360, 2899821596, 86897879520, 2604036564004, 78034199040600, 2338421934653996, 70074623840579280, 2099900293282724404, 62926934174641152840, 1885708124945951860796
OFFSET
1,2
LINKS
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.
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
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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