A042432 - OEIS

%I #16 Jun 13 2015 00:49:45

%S 27,82,109,191,300,491,791,1282,2073,7501,407127,1228882,1636009,

%T 2864891,4500900,7365791,11866691,19232482,31099173,112530001,

%U 6107719227,18435687682,24543406909,42979094591,67522501500,110501596091,178024097591,288525693682

%N Numerators of continued fraction convergents to sqrt(744).

%H Vincenzo Librandi, <a href="/A042432/b042432.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 (0,0,0,0,0,0,0,0,0,15002,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^19 -27*x^18 +82*x^17 -109*x^16 +191*x^15 -300*x^14 +491*x^13 -791*x^12 +1282*x^11 -2073*x^10 -7501*x^9 -2073*x^8 -1282*x^7 -791*x^6 -491*x^5 -300*x^4 -191*x^3 -109*x^2 -82*x -27) / (x^20 -15002*x^10 +1). - _Colin Barker_, Dec 14 2013

%t Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[744], n]]], {n, 1, 50}] (* _Artur Jasinski_, Dec 20 2008 *)

%t Numerator[Convergents[Sqrt[744], 30]] (* _Vincenzo Librandi_, Nov 24 2013 *)

%Y Cf. A042433, A040716.

%K nonn,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 14 2013