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.
From Vladeta Jovovic, Mar 25 2002: (Start)
a(n+1) = (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^2/(1-30*x+x^2). (End)
a(n) = 4 * sinh((n-1) * arccosh(15)) / sinh(arccosh(15)). - Andrés Ventas, Dec 21 2025
E.g.f.: 4 - exp(15*x)*(56*cosh(4*sqrt(14)*x) - 15*sqrt(14)*sinh(4*sqrt(14)*x))/14. - Stefano Spezia, Jan 05 2026
MAPLE
Digits := 1000: seq(floor(evalf(((15+4*sqrt(14))^(n-1)-(15-4*sqrt(14))^(n-1))/28*sqrt(14))+0.1), n=1..30);
MATHEMATICA
LinearRecurrence[{30, -1}, {0, 4}, 16] (* Ray Chandler, Aug 11 2015 *)
CROSSREFS
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