A042518 Numerators of continued fraction convergents to sqrt(788).

28, 393, 22036, 308897, 17320268, 242792649, 13613708612, 190834713217, 10700357648764, 149995841795913, 8410467498219892, 117896540816874401, 6610616753243186348, 92666531086221483273, 5195936357581646249636

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, 786, 0, -1).

Formula

G.f.: (28 + 393*x + 28*x^2 - x^3)/(1 - 786*x^2 + x^4). - Vincenzo Librandi, Nov 26 2013

a(n) = 786*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 26 2013

Mathematica

Numerator[Convergents[Sqrt[788], 30]] (* or *) CoefficientList[Series[(28 + 393 x + 28 x^2 - x^3)/(1 - 786 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 25 2013 *)

Prog

(Magma) I:=[28, 393, 22036, 308897]; [n le 4 select I[n] else 786*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 26 2013

Crossrefs

Cf. A042519.

Sequence in context: A126921 A035709 A035476 * A297179 A269255 A125463

Adjacent sequences: A042515 A042516 A042517 * A042519 A042520 A042521

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved