A042249 Denominators of continued fraction convergents to sqrt(650).

1, 2, 101, 204, 10301, 20806, 1050601, 2122008, 107151001, 216424010, 10928351501, 22073127012, 1114584702101, 2251242531214, 113676711262801, 229604665056816, 11593909964103601, 23417424593264018, 1182465139627304501, 2388347703847873020

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,102,0,-1).

Formula

G.f.: -(x^2-2*x-1) / ((x^2-10*x-1)*(x^2+10*x-1)). - Colin Barker, Dec 05 2013

a(n) = 102*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 18 2014

Mathematica

Denominator[Convergents[Sqrt[650], 30]] (* Harvey P. Dale, May 08 2012 *)
CoefficientList[Series[(1 + 2 x - x^2)/(x^4 - 102 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 18 2014 *)

Prog

(Magma) I:=[1, 2, 101, 204]; [n le 4 select I[n] else 102*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jan 18 2014

Crossrefs

Cf. A042248, A040624.

Sequence in context: A100669 A142050 A195903 * A157338 A064152 A162353

Adjacent sequences: A042246 A042247 A042248 * A042250 A042251 A042252

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Dec 05 2013

Status

approved