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
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).
Crossrefs
Cf. A089926. - R. J. Mathar, Sep 09 2008
Programs
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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 *)
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)