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A041513 Denominators of continued fraction convergents to sqrt(273). 2

%I #17 Sep 08 2022 08:44:54

%S 1,1,2,21,23,44,1431,1475,2906,30535,33441,63976,2080673,2144649,

%T 4225322,44397869,48623191,93021060,3025297111,3118318171,6143615282,

%U 64554470991,70698086273,135252557264,4398779918721,4534032475985,8932812394706,93862156423045

%N Denominators of continued fraction convergents to sqrt(273).

%H Vincenzo Librandi, <a href="/A041513/b041513.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 (0,0,0,0,0,1454,0,0,0,0,0,-1).

%F G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-22*x^3-1) / (x^12-1454*x^6+1). - _Colin Barker_, Nov 18 2013

%F a(n) = 1454*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 19 2013

%t Denominator[Convergents[Sqrt[273], 30]] (* _Vincenzo Librandi_, Dec 19 2013 *)

%t LinearRecurrence[{0,0,0,0,0,1454,0,0,0,0,0,-1},{1,1,2,21,23,44,1431,1475,2906,30535,33441,63976},30] (* _Harvey P. Dale_, Jun 15 2021 *)

%o (Magma) I:=[1,1,2,21,23,44,1431,1475,2906,30535,33441, 63976]; [n le 12 select I[n] else 1454*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Dec 19 2013

%Y Cf. A041512, A040256.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 18 2013

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)