A042920 Numerators of continued fraction convergents to sqrt(992).

31, 63, 3937, 7937, 496031, 999999, 62495969, 125991937, 7873996063, 15873984063, 992061007969, 1999996000001, 124991813008031, 251983622016063, 15747976378003937, 31747936378023937, 1984120031815488031, 3999988000008999999, 249983376032373487969

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, 126, 0, -1).

Formula

G.f.: (31 + 63*x + 31*x^2 - x^3)/(1 - 126*x^2 + x^4). - Vincenzo Librandi, Dec 09 2013

a(n) = 126*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 09 2013

Mathematica

Numerator[Convergents[Sqrt[992], 30]] (* or *) CoefficientList[Series[(31 + 63 x + 31 x^2 - x^3)/(1 - 126 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2013 *)

Prog

(Magma) I:=[31, 63, 3937, 7937]; [n le 4 select I[n] else 126*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 09 2013

Crossrefs

Cf. A042921.

Sequence in context: A042914 A042916 A042918 * A247438 A132772 A116324

Adjacent sequences: A042917 A042918 A042919 * A042921 A042922 A042923

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 09 2013

Status

approved