A041758 Numerators of continued fraction convergents to sqrt(399).

19, 20, 779, 799, 31141, 31940, 1244861, 1276801, 49763299, 51040100, 1989287099, 2040327199, 79521720661, 81562047860, 3178879539341, 3260441587201, 127075659852979, 130336101440180, 5079847514579819, 5210183616019999, 203066824923339781

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,40,0,-1).

Formula

G.f.: (19 + 20*x + 19*x^2 - x^3)/(1 - 40*x^2 + x^4). - Vincenzo Librandi, Nov 07 2013

a(n) = 40*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 07 2013

Mathematica

Numerator[Convergents[Sqrt[399], 30]] (* or *) CoefficientList[Series[(19 + 20 x + 19 x^2 - x^3)/(1 - 40 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 07 2013 *)
LinearRecurrence[{0, 40, 0, -1}, {19, 20, 779, 799}, 30] (* Harvey P. Dale, Sep 21 2018 *)

Prog

(Magma) I:=[19, 20, 779, 799]; [n le 4 select I[n] else 40*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 07 2013

Crossrefs

Cf. A041759.

Sequence in context: A041179 A041756 A041757 * A042735 A156758 A089837

Adjacent sequences: A041755 A041756 A041757 * A041759 A041760 A041761

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved