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A041426 Numerators of continued fraction convergents to sqrt(229). 10

%I

%S 15,106,121,227,1710,51527,362399,413926,776325,5848201,176222355,

%T 1239404686,1415627041,2655031727,20000849130,602680505627,

%U 4238764388519,4841444894146,9080209282665,68402909872801,2061167505466695,14496575448139666,16557742953606361

%N Numerators of continued fraction convergents to sqrt(229).

%C From _Johannes W. Meijer_, Jun 12 2010: (Start)

%C The a(n) terms of this sequence can be constructed with the terms of sequence A090301.

%C For the terms of the periodical sequence of the continued fraction for sqrt(229) see A040213. We observe that its period is five. (End)

%H Vincenzo Librandi, <a href="/A041426/b041426.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, 3420, 0, 0, 0, 0, 1).

%F From _Johannes W. Meijer_, Jun 12 2010: (Start)

%F a(5n) = A090301(3n+1), a(5n+1) = (A090301(3n+2) - A090301(3n+1))/2, a(5n+2) = (A090301(3n+2) + A090301(3n+1))/2, a(5n+3) = A090301(3n+2) and a(5n+4) = A090301(3n+3)/2. (End)

%F G.f.: -(x^9-15*x^8+106*x^7-121*x^6+227*x^5+1710*x^4+227*x^3+121*x^2+106*x+15) / (x^10+3420*x^5-1). - _Colin Barker_, Nov 08 2013

%t Numerator[Convergents[Sqrt[229], 30]] (* _Vincenzo Librandi_, Nov 01 2013 *)

%t LinearRecurrence[{0,0,0,0,3420,0,0,0,0,1},{15,106,121,227,1710,51527,362399,413926,776325,5848201},30] (* _Harvey P. Dale_, Dec 19 2016 *)

%Y Cf. A041427, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550.

%K nonn,frac,cofr,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 08 2013

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Last modified March 26 01:08 EDT 2019. Contains 321479 sequences. (Running on oeis4.)