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A042024 Numerators of continued fraction convergents to sqrt(536). 2

%I

%S 23,139,162,301,764,4121,9006,13127,22133,145925,6734683,40554023,

%T 47288706,87842729,222974164,1202713549,2628401262,3831114811,

%U 6459516073,42588211249,1965517233527,11835691612411

%N Numerators of continued fraction convergents to sqrt(536).

%H Vincenzo Librandi, <a href="/A042024/b042024.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 (0,0,0,0,0,0,0,0,0,291850,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: (23 +139*x +162*x^2 +301*x^3 +764*x^4 +4121*x^5 +9006*x^6 +13127*x^7 +22133*x^8 +145925*x^9 +22133*x^10 -13127*x^11 +9006*x^12 -4121*x^13 +764*x^14 -301*x^15 +162*x^16 -139*x^17 +23*x^18 -x^19) / (1 -291850*x^10 +x^20). - _Vincenzo Librandi_, Nov 13 2013

%F a(n) = 291850*a(n-10)-a(n-20): n in [1..30]]; // _Vincenzo Librandi_, Nov 14 2013

%t Numerator[Convergents[Sqrt[536], 30]] (* or *) CoefficientList[Series[(23 + 139 x + 162 x^2 + 301 x^3 + 764 x^4 + 4121 x^5 + 9006 x^6 + 13127 x^7 + 22133 x^8 + 145925 x^9 + 22133 x^10 - 13127 x^11 + 9006 x^12 - 4121 x^13 + 764 x^14 - 301 x^15 + 162 x^16 - 139 x^17 + 23 x^18 - x^19)/(1 - 291850 x^10 + x^20), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 14 2013 *)

%o (MAGMA) I:=[23,139,162,301,764,4121,9006,13127,22133,145925,6734683, 40554023,47288706,87842729,222974164,1202713549,2628401262,3831114811, 6459516073, 42588211249]; [n le 20 select I[n] else 291850*Self(n-10)-Self(n-20): n in [1..30]]; // _Vincenzo Librandi_, Nov 14 2013

%Y Cf. A042025.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

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Last modified August 12 17:17 EDT 2020. Contains 336439 sequences. (Running on oeis4.)