A042856 Numerators of continued fraction convergents to sqrt(959).

30, 31, 929, 960, 58529, 59489, 1783710, 1843199, 112375650, 114218849, 3424722271, 3538941120, 215761189471, 219300130591, 6575464976610, 6794765107201, 414261371408670, 421056136515871, 12624889330368929, 13045945466884800, 795381617343456929, 808427562810341729

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, 0, 1920, 0, 0, 0, -1).

Formula

G.f.: (30 + 31*x + 929*x^2 + 960*x^3 + 929*x^4 - 31*x^5 + 30*x^6 - x^7)/(1 - 1920*x^4 + x^8). - Vincenzo Librandi, Dec 07 2013

a(n) = 1920*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 07 2013

Mathematica

Numerator[Convergents[Sqrt[959], 30]] (* or *) CoefficientList[Series[(30 + 31 x + 929 x^2 + 960 x^3 + 929 x^4 - 31 x^5 + 30 x^6 - x^7)/(1 - 1920 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 07 2013 *)
LinearRecurrence[{0, 0, 0, 1920, 0, 0, 0, -1}, {30, 31, 929, 960, 58529, 59489, 1783710, 1843199}, 30] (* Harvey P. Dale, Apr 09 2015 *)

Prog

(Magma) I:=[ 30, 31, 929, 960, 58529, 59489, 1783710, 1843199 ]; [n le 8 select I[n] else 1920*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 07 2013

Crossrefs

Cf. A042857.

Sequence in context: A042852 A042854 A268337 * A042857 A042858 A175514

Adjacent sequences: A042853 A042854 A042855 * A042857 A042858 A042859

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 07 2013

Status

approved