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Numerators of continued fraction convergents to sqrt(34).
2

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

%S 5,6,29,35,379,414,2035,2449,26525,28974,142421,171395,1856371,

%T 2027766,9967435,11995201,129919445,141914646,697578029,839492675,

%U 9092504779,9931997454,48820494595,58752492049

%N Numerators of continued fraction convergents to sqrt(34).

%H Vincenzo Librandi, <a href="/A041056/b041056.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 (0,0,0,70,0,0,0,-1).

%F a(n) = 70*a(n-4)-a(n-8). G.f.: -(x^7-5*x^6+6*x^5-29*x^4-35*x^3-29*x^2-6*x-5)/(x^8-70*x^4+1). [_Colin Barker_, Jul 16 2012]

%t Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[34], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2011 *)

%t Numerator[Convergents[Sqrt[34],30]] (* _Harvey P. Dale_, Feb 17 2012 *)

%t CoefficientList[Series[- (x^7 - 5 x^6 + 6 x^5 - 29 x^4 - 35 x^3 - 29 x^2 - 6 x - 5)/(x^8 - 70 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 23 2013 *)

%Y Cf. A010489, A041057.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.