A042114 Numerators of continued fraction convergents to sqrt(582).

24, 193, 9288, 74497, 3585144, 28755649, 1383856296, 11099606017, 534164945112, 4284419166913, 206186284956936, 1653774698822401, 79587371828432184, 638352749326279873, 30720519339489866088

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, 386, 0, -1).

Formula

G.f.: (24 + 193*x + 24*x^2 - x^3)/(1 - 386*x^2 + x^4). - Vincenzo Librandi, Nov 16 2013

a(n) = 386*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 17 2013

Mathematica

Numerator[Convergents[Sqrt[582], 30]] (* or *) CoefficientList[Series[(24 + 193 x + 24 x^2 - x^3)/(1 - 386 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 17 2013 *)

Prog

(Magma) I:=[24, 193, 9288, 74497]; [n le 4 select I[n] else 386*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 17 2013

Crossrefs

Cf. A042115.

Sequence in context: A047057 A066406 A271432 * A220296 A282286 A123197

Adjacent sequences: A042111 A042112 A042113 * A042115 A042116 A042117

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved