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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 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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