A042510 Numerators of continued fraction convergents to sqrt(783).

27, 28, 1539, 1567, 86157, 87724, 4823253, 4910977, 270016011, 274926988, 15116073363, 15391000351, 846230092317, 861621092668, 47373769096389, 48235390189057, 2652084839305467, 2700320229494524

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,56,0,-1).

Formula

G.f.: (27 + 28*x + 27*x^2 - x^3)/(1 - 56*x^2 + x^4). - Vincenzo Librandi, Nov 26 2013

a(n) = 56*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 26 2013

Mathematica

Numerator[Convergents[Sqrt[783], 30]] (* or *) CoefficientList[Series[(27 + 28 x + 27 x^2 - x^3)/(1 - 56 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 25 2013 *)
LinearRecurrence[{0, 56, 0, -1}, {27, 28, 1539, 1567}, 30] (* Harvey P. Dale, Apr 28 2016 *)

Prog

(Magma) I:=[27, 28, 1539, 1567]; [n le 4 select I[n] else 56*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 26 2013

Crossrefs

Cf. A042511.

Sequence in context: A041363 A042508 A042509 * A157251 A214832 A090043

Adjacent sequences: A042507 A042508 A042509 * A042511 A042512 A042513

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved