A041391 Denominators of continued fraction convergents to sqrt(210).

1, 2, 57, 116, 3305, 6726, 191633, 389992, 11111409, 22612810, 644270089, 1311152988, 37356553753, 76024260494, 2166035847585, 4408095955664, 125592722606177, 255593541168018, 7282211875310681, 14820017291789380, 422242696045413321

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,58,0,-1).

Crossrefs

Cf. A041390, A176441, A040195.

Programs

Magma

I:=[1,2,57,116]; [n le 4 select I[n] else 58*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[210], 30]] (* Vincenzo Librandi, Dec 17 2013 *)

Formula

G.f.: -(x^2-2*x-1) / (x^4-58*x^2+1). - Colin Barker, Nov 17 2013

a(n) = 58*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 17 2013

Extensions

More terms from Colin Barker, Nov 17 2013