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%I #45 Feb 21 2023 07:34:57
%S 1,3,4,7,25,357,1096,1453,2549,9100,129949,398947,528896,927843,
%T 3312425,47301793,145217804,192519597,337737401,1205731800,
%U 17217982601,52859679603,70077662204,122937341807,438889687625,6267392968557,19241068593296,25508461561853
%N Denominators of continued fraction convergents to sqrt(53).
%C The terms of this sequence can be constructed with the terms of sequence A054413. For the terms of the periodic sequence of the continued fraction for sqrt(53) see A010139. We observe that its period is five. The decimal expansion of sqrt(53) is A010506. - _Johannes W. Meijer_, Jun 12 2010
%H Vincenzo Librandi, <a href="/A041091/b041091.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,364,0,0,0,0,1).
%F a(5*n) = A054413(3*n), a(5*n+1) = (A054413(3*n+1) - A054413(3*n))/2, a(5*n+2)= (A054413(3*n+1) + A054413(3*n))/2, a(5*n+3) = A054413(3*n+1) and a(5*n+4) = A054413(3*n+2)/2. - _Johannes W. Meijer_, Jun 12 2010
%F G.f.: -(x^8-3*x^7+4*x^6-7*x^5+25*x^4+7*x^3+4*x^2+3*x+1) / (x^10+364*x^5-1). - _Colin Barker_, Sep 26 2013
%p convert(sqrt(53), confrac, 30, cvgts): denom(cvgts); # _Wesley Ivan Hurt_, Dec 17 2013
%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[53], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 23 2011 *)
%t Denominator[Convergents[Sqrt[53], 30]] (* _Vincenzo Librandi_, Oct 24 2013 *)
%t LinearRecurrence[{0,0,0,0,364,0,0,0,0,1},{1,3,4,7,25,357,1096,1453,2549,9100},30] (* _Harvey P. Dale_, Nov 13 2019 *)
%Y Cf. A010506, A041090.
%Y Cf. A041019, A041047, A041151, A041227, A041319, A041427 and A041551. - _Johannes W. Meijer_, Jun 12 2010
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
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