A041081 Denominators of continued fraction convergents to sqrt(47).

1, 1, 6, 7, 90, 97, 575, 672, 8639, 9311, 55194, 64505, 829254, 893759, 5298049, 6191808, 79599745, 85791553, 508557510, 594349063, 7640746266, 8235095329, 48816222911, 57051318240, 733432041791, 790483360031, 4685848841946, 5476332201977, 70401835265670

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• frac

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,96,0,0,0,-1).

Crossrefs

Cf. A010501, A041080.

Programs

Magma

I:=[1, 1, 6, 7, 90, 97, 575, 672]; [n le 8 select I[n] else 96*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[47],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011 *)
CoefficientList[Series[(1 + x + 6 x^2 + 7 x^3 - 6 x^4 + x^5 - x^6)/(x^8 - 96 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)

Formula

G.f.: -(x^2-x-1)*(x^4+7*x^2+1) / (x^8-96*x^4+1). - Colin Barker, Nov 12 2013

a(n) = 96*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

Extensions

More terms from Colin Barker, Nov 12 2013