A041173 Denominators of continued fraction convergents to sqrt(96).

1, 1, 4, 5, 94, 99, 391, 490, 9211, 9701, 38314, 48015, 902584, 950599, 3754381, 4704980, 88444021, 93149001, 367891024, 461040025, 8666611474, 9127651499, 36049565971, 45177217470, 849239480431, 894416697901, 3532489574134, 4426906272035, 83216802470764

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,98,0,0,0,-1).

Formula

G.f.: (1 +x +4*x^2 +5*x^3 -4*x^4 +x^5 -x^6)/(1 -98*x^4 +x^8). - Vincenzo Librandi, Dec 12 2013

a(n) = 98*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 12 2013

Mathematica

  Denominator[Convergents[Sqrt[96], 201]] (* or *)  CoefficientList[Series[(1 + x + 4 x^2 + 5 x^3 - 4 x^4 + x^5 - x^6)/(1 - 98 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)

Prog

(Magma) I:=[1, 1, 4, 5, 94, 99, 391, 490]; [n le 8 select I[n] else 98*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Crossrefs

Cf. A041172.

Sequence in context: A109348 A192084 A078985 * A005512 A331584 A052320

Adjacent sequences: A041170 A041171 A041172 * A041174 A041175 A041176

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 12 2013

Status

approved