A042908 Numerators of continued fraction convergents to sqrt(986).

31, 63, 157, 9797, 19751, 49299, 3076289, 6201877, 15480043, 965964543, 1947409129, 4860782801, 303315942791, 611492668383, 1526301279557, 95242172000917, 192010645281391, 479263462563699, 29906345324230729, 60291954111025157, 150490253546281043

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, 0, 314, 0, 0, 1).

Formula

G.f.: (31 +63*x +157*x^2 +63*x^3 -31*x^4 +x^5)/(1 -314*x^3 -x^6). - Vincenzo Librandi, Dec 09 2013, simplified by Colin Barker, Dec 25 2013

a(n) = 314*a(n-3) + a(n-6). - Vincenzo Librandi, Dec 09 2013, simplified by Colin Barker, Dec 26 2013

Mathematica

Numerator[Convergents[Sqrt[986], 30]] (* or *) CoefficientList[Series[(31 + 63 x + 157 x^2 + 63 x^3 - 31 x^4 + x^5)/(1 - 314 x^3 - x^6), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2013 *)

Crossrefs

Cf. A042909, A040954.

Sequence in context: A042900 A239128 A042910 * A042912 A167783 A326381

Adjacent sequences: A042905 A042906 A042907 * A042909 A042910 A042911

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 09 2013

Status

approved