A042396 Numerators of continued fraction convergents to sqrt(725).

26, 27, 350, 727, 9074, 9801, 518726, 528527, 6861050, 14250627, 177868574, 192119201, 10168067026, 10360186227, 134490301750, 279340789727, 3486579778474, 3765920568201, 199314449324926

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, 0, 0, 0, 0, 19602, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^11 - 26*x^10 + 27*x^9 - 350*x^8 + 727*x^7 - 9074*x^6 - 9801*x^5 - 9074*x^4 - 727*x^3 - 350*x^2 - 27*x - 26)/(x^12 - 19602*x^6 + 1). - Vincenzo Librandi, Nov 23 2013

a(n) = 19602*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 23 2013

Mathematica

Numerator[Convergents[Sqrt[725], 30]] (* or *) CoefficientList[Series[-(x^11 - 26 x^10 + 27 x^9 - 350 x^8 + 727 x^7 - 9074 x^6 - 9801 x^5 - 9074 x^4 - 727 x^3 - 350 x^2 - 27 x - 26)/(x^12 - 19602 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2013 *)

Prog

(Magma) I:=[26, 27, 350, 727, 9074, 9801, 518726, 528527, 6861050, 14250627, 177868574, 192119201]; [n le 12 select I[n] else 19602*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 23 2013

Crossrefs

Cf. A042397.

Sequence in context: A042394 A137118 A137119 * A042398 A042400 A042401

Adjacent sequences: A042393 A042394 A042395 * A042397 A042398 A042399

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved