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A041060 Numerators of continued fraction convergents to sqrt(37). 2
6, 73, 882, 10657, 128766, 1555849, 18798954, 227143297, 2744518518, 33161365513, 400680904674, 4841332221601, 58496667563886, 706801342988233, 8540112783422682, 103188154744060417, 1246797969712147686 (list; graph; refs; listen; history; text; internal format)
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

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). [From Philippe Deléham, Nov 21 2008]

a(n)=3*{[6-sqrt(37)]^n+[6+sqrt(37)]^n}+(1/2)*sqrt(37)*{[6+sqrt(37)]^n-[6-sqrt(37)]^n }, with n>=0 [From Paolo P. Lava, Nov 28 2008]

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. [From R. J. Mathar, Sep 09 2008]

Sequence in context: A179568 A202557 * A089926 A135594 A168603 A244689

Adjacent sequences:  A041057 A041058 A041059 * A041061 A041062 A041063

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 30 22:27 EDT 2017. Contains 285686 sequences.