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%I #20 Jun 13 2015 00:49:21
%S 5,16,37,127,1307,4048,9403,32257,331973,1028176,2388325,8193151,
%T 84319835,261152656,606625147,2081028097,21416906117,66331746448,
%U 154080399013,528572943487,5439809833883,16848002445136
%N Numerators of continued fraction convergents to sqrt(28).
%H Vincenzo Librandi, <a href="/A041044/b041044.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 (0,0,0,254,0,0,0,-1).
%F a(n) = 254*a(n-4)-a(n-8). G.f.: -(x^7-5*x^6+16*x^5-37*x^4-127*x^3-37*x^2-16*x-5)/((x^4-16*x^2+1)*(x^4+16*x^2+1)). [_Colin Barker_, Jul 16 2012]
%t Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[28],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2011 *)
%t CoefficientList[Series[- (x^7 - 5 x^6 + 16 x^5 - 37 x^4 - 127 x^3 - 37 x^2 - 16 x - 5)/((x^4 - 16 x^2 + 1) (x^4 + 16 x^2 + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 22 2013 *)
%Y Cf. A010483, A041045.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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