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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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).

Crossrefs

Cf. A041172.

Programs

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

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 *)

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

Extensions

More terms from Vincenzo Librandi, Dec 12 2013