A042108 Numerators of continued fraction convergents to sqrt(579).

24, 385, 18504, 296449, 14248056, 228265345, 10970984616, 175764019201, 8447643906264, 135338066519425, 6504674836838664, 104210135455938049, 5008591176721865016, 80241668963005778305, 3856608701400999223656

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, 770, 0, -1).

Formula

G.f.: (24 + 385*x + 24*x^2 - x^3)/(1 - 770*x^2 + x^4). - Vincenzo Librandi, Nov 16 2013

a(n) = 770*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 16 2013

Mathematica

Numerator[Convergents[Sqrt[579], 30]] (* or *) CoefficientList[Series[(24 + 385 x + 24 x^2 - x^3)/(1 - 770 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)
LinearRecurrence[{0, 770, 0, -1}, {24, 385, 18504, 296449}, 20] (* Harvey P. Dale, Nov 06 2021 *)

Prog

(Magma) I:=[24, 385, 18504, 296449]; [n le 4 select I[n] else 770*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

Crossrefs

Cf. A042109.

Sequence in context: A020782 A025952 A028031 * A022455 A021954 A025950

Adjacent sequences: A042105 A042106 A042107 * A042109 A042110 A042111

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved