A041798 Numerators of continued fraction convergents to sqrt(420).

20, 41, 1660, 3361, 136100, 275561, 11158540, 22592641, 914864180, 1852321001, 75007704220, 151867729441, 6149716881860, 12451301493161, 504201776608300, 1020854854709761, 41338395964998740, 83697646784707241

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,82,0,-1).

Formula

G.f.: (20+41*x+20*x^2-x^3)/(1-82*x^2+x^4). - Vincenzo Librandi, Nov 09 2013

a(n) = 82*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 09 2013

Mathematica

Numerator[Convergents[Sqrt[420], 30]] (* or *) CoefficientList[Series[(20 + 41 x + 20 x^2 - x^3)/(1 - 82 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 09 2013 *)
LinearRecurrence[{0, 82, 0, -1}, {20, 41, 1660, 3361}, 30] (* Harvey P. Dale, Dec 16 2017 *)

Prog

(Magma) I:=[20, 41, 1660, 3361]; [n le 4 select I[n] else 82*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 09 2013

Crossrefs

Cf. A041799.

Sequence in context: A041792 A041794 A041796 * A132762 A075228 A256102

Adjacent sequences: A041795 A041796 A041797 * A041799 A041800 A041801

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved