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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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).

Crossrefs

Cf. A041759.

Programs

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

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 *)

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