A041159 Denominators of continued fraction convergents to sqrt(89).

1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000, 977001, 2007002, 6998007, 23001023, 53000053, 977001977, 2007004007, 6998013998, 23001046001, 53000106000, 977002954001, 2007006014002, 6998020996007, 23001069002023, 53000159000053, 977003931002977

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1000,0,0,0,0,1).

Formula

G.f.: -(x^8-2*x^7+7*x^6-23*x^5+53*x^4+23*x^3+7*x^2+2*x+1) / (x^10+1000*x^5-1). - Colin Barker, Nov 14 2013

a(n) = 1000*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 12 2013

Mathematica

Denominator/@Convergents[Sqrt[89], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^8 - 2 x^7 + 7 x^6 - 23 x^5 + 53 x^4 + 23 x^3 + 7 x^2 + 2 x + 1)/(x^10 + 1000 x^5 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)
LinearRecurrence[{0, 0, 0, 0, 1000, 0, 0, 0, 0, 1}, {1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000}, 30] (* Harvey P. Dale, Feb 07 2019 *)

Prog

(Magma) I:=[1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000]; [n le 10 select I[n] else 1000*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Crossrefs

Cf. A041158, A010161, A020846, A010540.

Sequence in context: A323526 A011757 A121963 * A210109 A034546 A281584

Adjacent sequences: A041156 A041157 A041158 * A041160 A041161 A041162

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved