A041223 Denominators of continued fraction convergents to sqrt(123).

1, 11, 243, 2684, 59291, 654885, 14466761, 159789256, 3529830393, 38987923579, 861264149131, 9512893564020, 210144922557571, 2321107041697301, 51274499839898193, 566340605280577424, 12510767816012601521, 138184786581419194155, 3052576072607234872931

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,244,0,-1).

Formula

G.f.: (1 + 11*x - x^2)/(1 - 244*x^2 + x^4). - Vincenzo Librandi, Dec 13 2013

a(n) = 244*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[123], 30]] (* or *) CoefficientList[Series[(1 + 11 x - x^2)/(1 - 244 x^2 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 244, 0, -1}, {1, 11, 243, 2684}, 20] (* Harvey P. Dale, Jul 27 2015 *)

Prog

(Magma) I:=[1, 11, 243, 2684]; [n le 4 select I[n] else 244*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041222.

Sequence in context: A267665 A196258 A121826 * A041220 A347483 A219089

Adjacent sequences: A041220 A041221 A041222 * A041224 A041225 A041226

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 13 2012

Status

approved