A042622 Numerators of continued fraction convergents to sqrt(840).

28, 29, 1652, 1681, 95788, 97469, 5554052, 5651521, 322039228, 327690749, 18672721172, 19000411921, 1082695788748, 1101696200669, 62777683026212, 63879379226881, 3640022919731548, 3703902298958429

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, 58, 0, -1).

Formula

G.f.: (28 +29*x +28*x^2 -x^3)/(1 -58*x^2 +x^4). - Vincenzo Librandi, Nov 29 2013

a(n) = 58*a(n-2) - a(n-4), - Vincenzo Librandi, Nov 29 2013

Mathematica

Numerator[Convergents[Sqrt[840], 30]] (* or *) CoefficientList[Series[(28 + 29 x + 28 x^2 - x^3)/(1 - 58 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 29 2013 *)
LinearRecurrence[{0, 58, 0, -1}, {28, 29, 1652, 1681}, 30] (* Harvey P. Dale, Oct 03 2014 *)

Prog

(Magma) I:=[28, 29, 1652, 1681]; [n le 4 select I[n] else 58*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 29 2013

Crossrefs

Cf. A042623.

Sequence in context: A042618 A042620 A042621 * A044977 A046466 A054396

Adjacent sequences: A042619 A042620 A042621 * A042623 A042624 A042625

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved