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

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,96,0,0,0,-1).

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

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 *)

Prog

(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

Crossrefs

Cf. A010501, A041080.

Sequence in context: A232008 A156791 A223532 * A041082 A036417 A267255

Adjacent sequences: A041078 A041079 A041080 * A041082 A041083 A041084

Keyword

nonn,cofr,easy,frac

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved