A042126 Numerators of continued fraction convergents to sqrt(588).

24, 97, 4680, 18817, 907896, 3650401, 176127144, 708158977, 34167758040, 137379191137, 6628368932616, 26650854921601, 1285869405169464, 5170128475599457, 249452036233943400, 1002978273411373057

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,194,0,-1).

Formula

G.f.: (24 + 97*x + 24*x^2 - x^3)/(1 - 194*x^2 + x^4). - Vincenzo Librandi, Nov 17 2013

a(n) = 194*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 17 2013

Mathematica

Numerator[Convergents[Sqrt[588], 30]] (* or *) CoefficientList[Series[(24 + 97 x + 24 x^2 - x^3)/(1 - 194 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 17 2013 *)
LinearRecurrence[{0, 194, 0, -1}, {24, 97, 4680, 18817}, 20] (* Harvey P. Dale, Jul 11 2023 *)

Prog

(Magma) I:=[24, 97, 4680, 18817]; [n le 4 select I[n] else 194*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 17 2013

Crossrefs

Cf. A042127.

Sequence in context: A225790 A042122 A042124 * A157514 A100152 A233405

Adjacent sequences: A042123 A042124 A042125 * A042127 A042128 A042129

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved