OFFSET
0,3
COMMENTS
46 is the smallest value of n for which the period of the continued fraction convergents to sqrt(n) is 12. [Colin Barker, Jul 19 2012]
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A. J. van der Poorten, An introduction to continued fractions, Unpublished.
A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]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).
FORMULA
a(n) = 48670*a(n-12)-a(n-24). G.f.: -(x^22 -x^21 +4*x^20 -5*x^19 +9*x^18 -23*x^17 +147*x^16 -317*x^15 +464*x^14 -781*x^13 +2807*x^12 -3588*x^11 -2807*x^10 -781*x^9 -464*x^8 -317*x^7 -147*x^6 -23*x^5 -9*x^4 -5*x^3 -4*x^2 -x -1) / (x^24-48670*x^12+1). [Colin Barker, Jul 19 2012]
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[46], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*)
Denominator[Convergents[Sqrt[46], 30]] (* Vincenzo Librandi, Oct 24 2013 *)
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
Formula corrected by Colin Barker, Jul 24 2012
STATUS
approved