A042102 Numerators of continued fraction convergents to sqrt(575).

23, 24, 1127, 1151, 54073, 55224, 2594377, 2649601, 124476023, 127125624, 5972254727, 6099380351, 286543750873, 292643131224, 13748127787177, 14040770918401, 659623590033623, 673664360952024

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,48,0,-1).

Formula

G.f.: -(x^3 - 23*x^2 - 24*x - 23)/(x^4 - 48*x^2 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 48*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 12 2013

Mathematica

Numerator[Convergents[Sqrt[575], 20]] (* Harvey P. Dale, Aug 10 2011 *)
CoefficientList[Series[-(x^3 - 23 x^2 - 24 x - 23)/(x^4 - 48 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)

Prog

(Magma) I:=[23, 24, 1127, 1151]; [n le 4 select I[n] else 48*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

Crossrefs

Cf. A042103.

Sequence in context: A041263 A042100 A042101 * A156964 A147624 A263315

Adjacent sequences: A042099 A042100 A042101 * A042103 A042104 A042105

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved