A042680 Numerators of continued fraction convergents to sqrt(870).

29, 59, 3451, 6961, 407189, 821339, 48044851, 96911041, 5668885229, 11434681499, 668880412171, 1349195505841, 78922219750949, 159193635007739, 9312153050199811, 18783499735407361, 1098755137703826749

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,118,0,-1).

Formula

G.f.: (29 +59*x +29*x^2 -x^3)/(1 -118*x^2 +x^4). - Vincenzo Librandi, Dec 01 2013

a(n) = 118*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 01 2013

Mathematica

Numerator[Convergents[Sqrt[870], 30]] (* Harvey P. Dale, Oct 11 2012 *)
CoefficientList[Series[(29 + 59 x + 29 x^2 - x^3)/(1 - 118 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 01 2013 *)

Prog

(Magma) I:=[29, 59, 3451, 6961]; [n le 4 select I[n] else 118*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 01 2013

Crossrefs

Cf. A042681.

Sequence in context: A042676 A124643 A042678 * A286005 A132770 A141111

Adjacent sequences: A042677 A042678 A042679 * A042681 A042682 A042683

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved