A041407 Denominators of continued fraction convergents to sqrt(218).

1, 1, 4, 13, 17, 489, 506, 2007, 6527, 8534, 245479, 254013, 1007518, 3276567, 4284085, 123230947, 127515032, 505776043, 1644843161, 2150619204, 61862180873, 64012800077, 253900581104, 825714543389, 1079615124493, 31054938029193, 32134553153686

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,502,0,0,0,0,1).

Formula

G.f.: -(x^8-x^7+4*x^6-13*x^5+17*x^4+13*x^3+4*x^2+x+1) / (x^10+502*x^5-1). - Colin Barker, Nov 17 2013

a(n) = 502*a(n-5) + a(n-10) for n>9. - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[218], 30]] (* Vincenzo Librandi, Dec 17 2013 *)
LinearRecurrence[{0, 0, 0, 0, 502, 0, 0, 0, 0, 1}, {1, 1, 4, 13, 17, 489, 506, 2007, 6527, 8534}, 30] (* Harvey P. Dale, Jul 26 2014 *)

Prog

(Magma) I:=[1, 1, 4, 13, 17, 489, 506, 2007, 6527, 8534]; [n le 10 select I[n] else 502*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041406, A040203.

Sequence in context: A190122 A042713 A154130 * A252976 A065564 A332377

Adjacent sequences: A041404 A041405 A041406 * A041408 A041409 A041410

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved