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

0,2

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A041148, A040074, A020841, A010535.

Sequence in context: A368851 A337580 A288629 * A193810 A217987 A119814

Adjacent sequences: A041146 A041147 A041148 * A041150 A041151 A041152

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved