A042438 Numerators of continued fraction convergents to sqrt(747).

27, 82, 4455, 13447, 730593, 2205226, 119812797, 361643617, 19648568115, 59307347962, 3222245358063, 9726043422151, 528428590154217, 1595011813884802, 86659066539933525, 261572211433685377

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0, 164, 0, -1).

Formula

G.f.: (27 + 82*x + 27*x^2 - x^3)/(1 - 164*x^2 + x^4), - Vincenzo Librandi, Nov 24 2013

a(n) = 164*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 24 2013

Mathematica

Numerator[Convergents[Sqrt[747], 30]] (* or *) CoefficientList[Series[(27 + 82 x + 27 x^2 - x^3)/(1 - 164 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 24 2013 *)

Prog

(Magma) I:=[27, 82, 4455, 13447]; [n le 4 select I[n] else 164*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 24 2013

Crossrefs

Cf. A042439.

Sequence in context: A195028 A042434 A042436 * A251088 A044981 A251081

Adjacent sequences: A042435 A042436 A042437 * A042439 A042440 A042441

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved