A041844 Numerators of continued fraction convergents to sqrt(444).

21, 295, 12411, 174049, 7322469, 102688615, 4320244299, 60586108801, 2548936813941, 35745701503975, 1503868399980891, 21089903301236449, 887279807051911749, 12443007202028000935, 523493582292227951019

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,590,0,-1).

Formula

G.f.: -(x^3-21*x^2-295*x-21)/(x^4-590*x^2+1). - Vincenzo Librandi, Nov 10 2013

a(n) = 590*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[444], 20]] (* Harvey P. Dale, Oct 01 2013 *)
CoefficientList[Series[-(x^3 - 21 x^2 - 295 x - 21)/(x^4 - 590 x^2 + 1), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 10 2013 *)

Prog

(Magma) I:=[21, 295, 12411, 174049]; [n le 4 select I[n] else 590*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 10 2013

Crossrefs

Cf. A041845.

Sequence in context: A021864 A020570 A025940 * A295779 A021829 A019943

Adjacent sequences: A041841 A041842 A041843 * A041845 A041846 A041847

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved