A041079 Denominators of continued fraction convergents to sqrt(46).

1, 1, 4, 5, 9, 23, 147, 317, 464, 781, 2807, 3588, 45863, 49451, 194216, 243667, 437883, 1119433, 7154481, 15428395, 22582876, 38011271, 136616689, 174627960, 2232152209, 2406780169, 9452492716, 11859272885

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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• A. J. van der Poorten, An introduction to continued fractions, Unpublished.
• A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]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).

Crossrefs

Cf. A010500, A041078.

Programs

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 *)

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]

Extensions

Formula corrected by Colin Barker, Jul 24 2012