A041149 Denominators of continued fraction convergents to sqrt(84).

1, 6, 109, 660, 11989, 72594, 1318681, 7984680, 145042921, 878242206, 15953402629, 96598657980, 1754729246269, 10624974135594, 193004263686961, 1168650556257360, 21228714276319441, 128540936214174006, 2334965566131451549, 14138334333002883300

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 (0,110,0,-1).

Crossrefs

Cf. A041148, A040074, A020841, A010535.

Programs

Magma

I:=[1, 6, 109, 660]; [n le 4 select I[n] else 110*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator/@Convergents[Sqrt[84], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[(1 + 6 x - x^2)/(x^4 - 110 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)

Formula

G.f.: -(x^2-6*x-1) / (x^4-110*x^2+1). - Colin Barker, Nov 13 2013

a(n) = 110*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013