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Numerators of continued fraction convergents to sqrt(33).
2

%I #24 Jun 13 2015 00:49:21

%S 5,6,17,23,247,270,787,1057,11357,12414,36185,48599,522175,570774,

%T 1663723,2234497,24008693,26243190,76495073,102738263,1103877703,

%U 1206615966,3517109635,4723725601,50754365645

%N Numerators of continued fraction convergents to sqrt(33).

%H Vincenzo Librandi, <a href="/A041054/b041054.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,46,0,0,0,-1).

%F a(n) = 46*a(n-4)-a(n-8). G.f.: -(x^7-5*x^6+6*x^5-17*x^4-23*x^3-17*x^2-6*x-5)/(x^8-46*x^4+1). [_Colin Barker_, Jul 16 2012]

%t Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[33], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2011 *)

%t Numerator[Convergents[Sqrt[33],30]] (* _Harvey P. Dale_, Oct 25 2011 *)

%t CoefficientList[Series[- (x^7 - 5 x^6 + 6 x^5 - 17 x^4 - 23 x^3 - 17 x^2 - 6 x - 5)/(x^8 - 46 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 23 2013 *)

%Y Cf. A010488, A041055.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.