A042917 Denominators of continued fraction convergents to sqrt(990).

1, 2, 13, 28, 1749, 3526, 22905, 49336, 3081737, 6212810, 40358597, 86930004, 5430018845, 10946967694, 71111825009, 153170617712, 9567690123153, 19288550864018, 125298995307261, 269886541478540, 16858264566976741, 33986415675432022, 220776758619568873

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1762,0,0,0,-1).

Formula

G.f.: -(x^2-2*x-1)*(x^4+14*x^2+1) / ((x^4-42*x^2+1)*(x^4+42*x^2+1)). - Colin Barker, Dec 25 2013

a(n) = 1762*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Feb 01 2014

Mathematica

Denominator[Convergents[Sqrt[990], 30]] (* Vincenzo Librandi, Feb 01 2014 *)

Prog

(Magma) I:=[1, 2, 13, 28, 1749, 3526, 22905, 49336]; [n le 8 select I[n] else 1762*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Feb 01 2014

Crossrefs

Cf. A042916, A040958.

Sequence in context: A041017 A033837 A041575 * A366720 A174049 A141336

Adjacent sequences: A042914 A042915 A042916 * A042918 A042919 A042920

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 25 2013

Status

approved