A042514 Numerators of continued fraction convergents to sqrt(786).

28, 785, 43988, 1232449, 69061132, 1934944145, 108425933252, 3037861075201, 170228646144508, 4769439953121425, 267258866020944308, 7488017688539562049, 419596249424236419052, 11756183001567159295505

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1570,0,-1).

Formula

a(n) = (28 + 785*x + 28*x^2 - x^3)/(1 - 1570*x^2 + x^4). - Vincenzo Librandi, Nov 26 2013

a(n) = 1570*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 26 2013

Mathematica

Numerator[Convergents[Sqrt[786], 30]] (* or *) CoefficientList[Series[(28 + 785 x + 28 x^2 - x^3)/(1 - 1570 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 25 2013 *)
LinearRecurrence[{0, 1570, 0, -1}, {28, 785, 43988, 1232449}, 20] (* Harvey P. Dale, Feb 24 2015 *)

Prog

(Magma) I:=[28, 785, 43988, 1232449]; [n le 4 select I[n] else 1570*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 26 2013

Crossrefs

Cf. A042515.

Sequence in context: A009972 A114037 A041365 * A158659 A214133 A119055

Adjacent sequences: A042511 A042512 A042513 * A042515 A042516 A042517

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved