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A041345 Denominators of continued fraction convergents to sqrt(186). 2

%I #16 Sep 08 2022 08:44:54

%S 1,1,2,3,11,47,152,199,351,550,14651,15201,29852,45053,165011,705097,

%T 2280302,2985399,5265701,8251100,219794301,228045401,447839702,

%U 675885103,2475495011,10577865147,34209090452,44786955599,78996046051,123783001650

%N Denominators of continued fraction convergents to sqrt(186).

%H Vincenzo Librandi, <a href="/A041345/b041345.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 (0,0,0,0,0,0,0,0,0,15002,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^18 -x^17 +2*x^16 -3*x^15 +11*x^14 -47*x^13 +152*x^12 -199*x^11 +351*x^10 -550*x^9 -351*x^8 -199*x^7 -152*x^6 -47*x^5 -11*x^4 -3*x^3 -2*x^2 -x -1) / (x^20 -15002*x^10 +1). - _Colin Barker_, Nov 15 2013

%F a(n) = 15002*a(n-10) - a(n-20). - _Vincenzo Librandi_, Dec 16 2013

%t Denominator[Convergents[Sqrt[186], 30]] (* _Vincenzo Librandi_, Dec 16 2013 *)

%o (Magma) I:=[1,1,2,3,11,47,152,199,351,550,14651,15201, 29852,45053,165011,705097,2280302,2985399,5265701, 8251100]; [n le 20 select I[n] else 15002*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 16 2013

%Y Cf. A041344, A010228.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 15 2013

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)