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A041078 Numerators of continued fraction convergents to sqrt(46). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
A. J. van der Poorten, An introduction to continued fractions, Unpublished.
A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]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).
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
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 *)
CROSSREFS
Sequence in context: A259088 A200179 A054289 * A067229 A291606 A041535
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
Formula corrected by Colin Barker, Jul 24 2012
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)