A042106 Numerators of continued fraction convergents to sqrt(578).

24, 577, 27720, 665857, 31988856, 768398401, 36915112104, 886731088897, 42600007379160, 1023286908188737, 49160371600438536, 1180872205318713601, 56731026226898691384, 1362725501650887306817, 65467555105469489418600

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1154,0,-1).

Formula

G.f.: -(x^3 - 24*x^2 - 577*x - 24)/(x^4 - 1154*x^2 + 1). - Vincenzo Librandi, Nov 16 2013

a(n) = 1154*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 16 2013

Mathematica

Numerator[Convergents[Sqrt[578], 30]] (* or *) CoefficientList[Series[-(x^3 - 24 x^2 - 577 x - 24)/(x^4 - 1154 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)
LinearRecurrence[{0, 1154, 0, -1}, {24, 577, 27720, 665857}, 20] (* Harvey P. Dale, Jul 04 2015 *)

Prog

(Magma) I:=[24, 577, 27720, 665857]; [n le 4 select I[n] else 1154*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013

Crossrefs

Cf. A042107.

Sequence in context: A268027 A009968 A041265 * A158637 A179059 A334281

Adjacent sequences: A042103 A042104 A042105 * A042107 A042108 A042109

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved