A041842 Numerators of continued fraction convergents to sqrt(443).

21, 442, 18585, 390727, 16429119, 345402226, 14523322611, 305335177057, 12838600759005, 269915951116162, 11349308547637809, 238605395451510151, 10032775917511064151, 210926899663183857322, 8868962561771233071675

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, 884, 0, -1).

Formula

G.f.: -(x^3-21*x^2-442*x-21)/(x^4-884*x^2+1). - Vincenzo Librandi, Nov 10 2013

a(n) = 884*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[443], 30]] (* or *) CoefficientList[Series[-(x^3 - 21 x^2 - 442 x - 21)/(x^4 - 884 x^2 + 1), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 10 2013 *)

Prog

(Magma) I:=[21, 442, 18585, 390727]; [n le 4 select I[n] else 884*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 10 2013

Crossrefs

Cf. A041843.

Sequence in context: A009965 A285873 A189433 * A215152 A199252 A199197

Adjacent sequences: A041839 A041840 A041841 * A041843 A041844 A041845

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved