A041845 Denominators of continued fraction convergents to sqrt(444).

1, 14, 589, 8260, 347509, 4873386, 205029721, 2875289480, 120967187881, 1696415919814, 71370435820069, 1000882517400780, 42108436166652829, 590518988850540386, 24843905967889349041, 348405202539301426960, 14657862412618549281361, 205558478979198991366014

Offset

0,2

Links

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

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

Formula

G.f.: -(x^2-14*x-1) / (x^4-590*x^2+1). - Colin Barker, Nov 26 2013

a(n) = 590*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 25 2013

Mathematica

Denominator[Convergents[Sqrt[444], 30]] (* Vincenzo Librandi, Dec 25 2013 *)
LinearRecurrence[{0, 590, 0, -1}, {1, 14, 589, 8260}, 20] (* Harvey P. Dale, Aug 07 2022 *)

Prog

(Magma) I:=[1, 14, 589, 8260]; [n le 4 select I[n] else 590*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 25 2013

Crossrefs

Cf. A041844, A040422.

Sequence in context: A232369 A218412 A129007 * A205327 A291121 A279294

Adjacent sequences: A041842 A041843 A041844 * A041846 A041847 A041848

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 26 2013

Status

approved