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A041084 Numerators of continued fraction convergents to sqrt(50). 2

%I

%S 7,99,1393,19601,275807,3880899,54608393,768398401,10812186007,

%T 152139002499,2140758220993,30122754096401,423859315570607,

%U 5964153172084899,83922003724759193,1180872205318713601,16616132878186749607,233806732499933208099,3289910387877251662993

%N Numerators of continued fraction convergents to sqrt(50).

%H Vincenzo Librandi, <a href="/A041084/b041084.txt">Table of n, a(n) for n = 0..200</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (14,1).

%F a(n) = 14*a(n-1)+a(n-2), n>1 ; a(0)=7, a(1)=99 . G.f.: (7+x)/(1-14*x-x^2). - _Philippe Deléham_, Nov 21 2008

%F a(n) = (5/2)*sqrt(2)*{[7+5*sqrt(2)]^n-[7-5*sqrt(2)]^n}+(7/2)*{[7+5*sqrt(2)]^n +[7-5*sqrt(2)]^n}, with n>=0. - _Paolo P. Lava_, Nov 28 2008

%t Numerator[Convergents[Sqrt[50],30]] (* or *) LinearRecurrence[{14,1},{7,99},30] (* _Harvey P. Dale_, Aug 18 2013 *)

%t CoefficientList[Series[(7 + x)/(1 - 14 x - x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 29 2013 *)

%Y Cf. A010503, A041085.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 04 2013

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Last modified October 15 04:32 EDT 2018. Contains 316200 sequences. (Running on oeis4.)