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

0,1

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).

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

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 *)

Crossrefs

Cf. A041051, A010486.

Sequence in context: A042493 A042217 A041355 * A332523 A041227 A042183

Adjacent sequences: A041047 A041048 A041049 * A041051 A041052 A041053

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved