A041270 Numerators of continued fraction convergents to sqrt(148).

12, 73, 1764, 10657, 257532, 1555849, 37597908, 227143297, 5489037036, 33161365513, 801361809348, 4841332221601, 116993335127772, 706801342988233, 17080225566845364, 103188154744060417, 2493595939424295372

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,146,0,-1).

Formula

G.f.: (12+73*x+12*x^2-x^3)/(1-146*x^2+x^4). - Vincenzo Librandi, Nov 01 2013

a(n) = 146*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 01 2013

Mathematica

Numerator[Convergents[Sqrt[148], 30]] (* or *) CoefficientList[Series[(12 + 73 x + 12 x^2 - x^3)/(1 - 146 x^2 + x^4), {x, 0, 25}], x](* Vincenzo Librandi, Nov 01 2013 *)
LinearRecurrence[{0, 146, 0, -1}, {12, 73, 1764, 10657}, 20] (* Harvey P. Dale, Apr 28 2018 *)

Prog

(Magma) I:=[12, 73, 1764, 10657]; [n le 4 select I[n] else 146*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 01 2013

Crossrefs

Cf. A041271.

Sequence in context: A024014 A069039 A156196 * A055912 A346446 A064121

Adjacent sequences: A041267 A041268 A041269 * A041271 A041272 A041273

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved