A041078 Numerators of continued fraction convergents to sqrt(46).
6, 7, 27, 34, 61, 156, 997, 2150, 3147, 5297, 19038, 24335, 311058, 335393, 1317237, 1652630, 2969867, 7592364, 48524051, 104640466, 153164517, 257804983, 926579466, 1184384449, 15139192854, 16323577303
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- A. J. van der Poorten, An introduction to continued fractions, Unpublished.
- A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,48670,0,0,0,0,0,0,0,0,0,0,0,-1).
Programs
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Mathematica
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[46],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011 *) Numerator[Convergents[Sqrt[46], 30]] (* Vincenzo Librandi, Oct 25 2013 *)
Formula
a(n) = 48670*a(n-12)-a(n-24). G.f.: -(x^23 -6*x^22 +7*x^21 -27*x^20 +34*x^19 -61*x^18 +156*x^17 -997*x^16 +2150*x^15 -3147*x^14 +5297*x^13 -19038*x^12 -24335*x^11 -19038*x^10 -5297*x^9 -3147*x^8 -2150*x^7 -997*x^6 -156*x^5 -61*x^4 -34*x^3 -27*x^2 -7*x-6) / (x^24-48670*x^12+1). - Colin Barker, Jul 19 2012
Extensions
Formula corrected by Colin Barker, Jul 24 2012