A041428 Numerators of continued fraction convergents to sqrt(230).

15, 91, 2745, 16561, 499575, 3014011, 90919905, 548533441, 16546923135, 99830072251, 3011449090665, 18168524616241, 548067187577895, 3306571650083611, 99745216690086225, 601777871790600961

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,182,0,-1).

Crossrefs

Cf. A041429.

Programs

Mathematica

Numerator[Convergents[Sqrt[230], 20]] (* Harvey P. Dale, Jun 12 2012 *)
CoefficientList[Series[-(x^3 - 15 x^2 - 91 x - 15)/(x^4 -182 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 02 2013 *)

Formula

G.f.: -(x^3 -15*x^2 -91*x -15)/(x^4 -182*x^2 +1). - Vincenzo Librandi, Nov 02 2013

a(n) = 182*a(n-2) - a(n-4). - Wesley Ivan Hurt, May 04 2024