A041850 Numerators of continued fraction convergents to sqrt(447).

21, 148, 6237, 43807, 1846131, 12966724, 546448539, 3838106497, 161746921413, 1136066556388, 47876542289709, 336271862584351, 14171294770832451, 99535335258411508, 4194655375624115787

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,296,0,-1).

Formula

G.f.: -(x^3 - 21*x^2 - 148*x - 21)/(x^4 - 296*x^2 + 1). - Vincenzo Librandi, Nov 10 2013

a(n) = 296*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[447], 30]] (* Harvey P. Dale, Oct 08 2012 *)
CoefficientList[Series[-(x^3 - 21 x^2 - 148 x - 21)/(x^4 - 296 x^2 + 1), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 10 2013 *)

Prog

(Magma) I:=[21, 148, 6237, 43807]; [n le 4 select I[n] else 296*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 10 2013

Crossrefs

Cf. A041851.

Sequence in context: A198183 A259493 A253459 * A239123 A241697 A358994

Adjacent sequences: A041847 A041848 A041849 * A041851 A041852 A041853

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane

Status

approved