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Denominators of continued fraction convergents to sqrt(339).
2

%I #19 May 25 2024 13:58:52

%S 1,2,5,12,17,301,318,937,2192,5321,193748,392817,979382,2351581,

%T 3330963,58977952,62308915,183595782,429500479,1042596740,37962983119,

%U 76968562978,191900109075,460768781128,652668890203,11556139914579,12208808804782

%N Denominators of continued fraction convergents to sqrt(339).

%H Vincenzo Librandi, <a href="/A041641/b041641.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 (0,0,0,0,0,0,0,0,0,195940,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^18 -2*x^17 +5*x^16 -12*x^15 +17*x^14 -301*x^13 +318*x^12 -937*x^11 +2192*x^10 -5321*x^9 -2192*x^8 -937*x^7 -318*x^6 -301*x^5 -17*x^4 -12*x^3 -5*x^2 -2*x -1) / (x^20 -195940*x^10 +1). - _Colin Barker_, Nov 20 2013

%F a(n) = 195940*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 22 2013

%t Denominator[Convergents[Sqrt[339], 30]] (* _Vincenzo Librandi_, Dec 22 2013 *)

%o (Magma) I:=[1,2,5,12,17,301,318,937,2192,5321,193748,392817, 979382,2351581,3330963,58977952,62308915,183595782, 429500479,1042596740]; [n le 20 select I[n] else 195940*Self(n-10) - Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013

%Y Cf. A041640, A040320.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 20 2013