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A041842 Numerators of continued fraction convergents to sqrt(443). 2
21, 442, 18585, 390727, 16429119, 345402226, 14523322611, 305335177057, 12838600759005, 269915951116162, 11349308547637809, 238605395451510151, 10032775917511064151, 210926899663183857322, 8868962561771233071675 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 18 17:21 EST 2019. Contains 329287 sequences. (Running on oeis4.)