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Numerators of continued fraction convergents to sqrt(31).
2

%I #19 Jun 13 2015 00:49:21

%S 5,6,11,39,206,657,863,1520,16063,17583,33646,118521,626251,1997274,

%T 2623525,4620799,48831515,53452314,102283829,360303801,1903802834,

%U 6071712303,7975515137,14047227440,148447789537

%N Numerators of continued fraction convergents to sqrt(31).

%H Vincenzo Librandi, <a href="/A041050/b041050.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,3040,0,0,0,0,0,0,0,-1).

%F 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

%t Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[31],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2011*)

%t Numerator[Convergents[Sqrt[31], 30]] (* _Vincenzo Librandi_, Oct 28 2013 *)

%Y Cf. A041051, A010486.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.