A041433 Denominators of continued fraction convergents to sqrt(232).

1, 4, 13, 95, 298, 1287, 38908, 156919, 509665, 3724574, 11683387, 50458122, 1525427047, 6152166310, 19981925977, 146025648149, 458058870424, 1978261129845, 59805892765774, 241201832192941, 783411389344597, 5725081557605120, 17958656062159957

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,39206,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-4*x^9+13*x^8-95*x^7+298*x^6-1287*x^5-298*x^4-95*x^3-13*x^2-4*x-1) / ((x^6-198*x^3-1)*(x^6+198*x^3-1)). - Colin Barker, Nov 17 2013

a(n) = 39206*a(n-6) - a(n-12) for n>7. - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator[Convergents[Sqrt[232], 30]] (* Vincenzo Librandi, Dec 17 2013 *)

Prog

(Magma) I:=[1, 4, 13, 95, 298, 1287, 38908, 156919, 509665, 3724574, 11683387, 50458122]; [n le 12 select I[n] else 39206*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041432, A040216.

Sequence in context: A281182 A200850 A326565 * A222764 A058014 A290392

Adjacent sequences: A041430 A041431 A041432 * A041434 A041435 A041436

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved