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%I #29 Jun 10 2021 11:36:59
%S 5,11,16,27,70,727,1524,2251,3775,9801,101785,213371,315156,528527,
%T 1372210,14250627,29873464,44124091,73997555,192119201,1995189565,
%U 4182498331,6177687896,10360186227,26898060350
%N Numerators of continued fraction convergents to sqrt(29).
%C From _Johannes W. Meijer_, Jun 12 2010: (Start)
%C The terms of this sequence can be constructed with the terms of sequence A087130.
%C For the terms of the periodical sequence of the continued fraction for sqrt(29) see A010128. We observe that its period is five. The decimal expansion of sqrt(29) is A010484. (End)
%H Vincenzo Librandi, <a href="/A041046/b041046.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 (0,0,0,0,140,0,0,0,0,1).
%F a(5*n) = A087130(3*n+1), a(5*n+1) = (A087130(3*n+2) - A087130(3*n+1))/2, a(5*n+2) = ( A087130(3*n+2) + A087130(3*n+1))/2, a(5*n+3) = A087130(3*n+2) and a(5*n+4) = A087130(3*n+3)/2. - _Johannes W. Meijer_, Jun 12 2010
%F G.f.: (5 + 11*x + 16*x^2 + 27*x^3 + 70*x^4 + 27*x^5 - 16*x^6 + 11*x^7 - 5*x^8 + x^9)/(1 - 140*x^5 - x^10) - _Peter J. C. Moses_, Jul 29 2013
%t Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[29],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2011 *)
%t Numerator[Convergents[Sqrt[29], 30]] (* _Vincenzo Librandi_, Oct 28 2013 *)
%t LinearRecurrence[ {0,0,0,0,140,0,0,0,0,1},{5,11,16,27,70,727,1524,2251,3775,9801},30] (* _Harvey P. Dale_, Jun 10 2021 *)
%Y Cf. A041047, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550, A010484.
%K nonn,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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