A041050 Numerators of continued fraction convergents to sqrt(31).

5, 6, 11, 39, 206, 657, 863, 1520, 16063, 17583, 33646, 118521, 626251, 1997274, 2623525, 4620799, 48831515, 53452314, 102283829, 360303801, 1903802834, 6071712303, 7975515137, 14047227440, 148447789537

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,3040,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A041051, A010486.

Programs

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[31],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011*)
Numerator[Convergents[Sqrt[31], 30]] (* Vincenzo Librandi, Oct 28 2013 *)

Formula

G.f.: -(x^15 -5*x^14 +6*x^13 -11*x^12 +39*x^11 -206*x^10 +657*x^9 -863*x^8 -1520*x^7 -863*x^6 -657*x^5 -206*x^4 -39*x^3 -11*x^2 -6*x -5) / (x^16 -3040*x^8 +1). - Colin Barker, Nov 04 2013