A041060 Numerators of continued fraction convergents to sqrt(37).

6, 73, 882, 10657, 128766, 1555849, 18798954, 227143297, 2744518518, 33161365513, 400680904674, 4841332221601, 58496667563886, 706801342988233, 8540112783422682, 103188154744060417, 1246797969712147686

Offset

0,1

Links

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

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (12,1).

Formula

From Philippe Deléham, Nov 21 2008: (Start)

a(n) = 12*a(n-1) + a(n-2), n > 1; a(0)=6, a(1)=73.

G.f.: (6+x)/(1-12*x-x^2). (End)

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[37], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011 *)
CoefficientList[Series[(6 + x)/(1 - 12  x - x^2), {x, 0, 30}], x]  (* Vincenzo Librandi_, Oct 28 2013 *)

Crossrefs

Cf. A010491, A041061.

Cf. A089926. - R. J. Mathar, Sep 09 2008

Sequence in context: A105324 A179568 A202557 * A089926 A135594 A346960

Adjacent sequences: A041057 A041058 A041059 * A041061 A041062 A041063

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved