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Denominators of continued fraction convergents to sqrt(55).
2

%I #16 Nov 24 2022 12:53:05

%S 1,2,5,12,173,358,889,2136,30793,63722,158237,380196,5480981,11342158,

%T 28165297,67672752,975583825,2018840402,5013264629,12045369660,

%U 173648439869,359342249398,892332938665,2144008126728,30908446712857,63960901552442,158830249817741

%N Denominators of continued fraction convergents to sqrt(55).

%H Vincenzo Librandi, <a href="/A041095/b041095.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 (0,0,0,178,0,0,0,-1).

%F G.f.: -(x^2-2*x-1)*(x^4+6*x^2+1) / (x^8-178*x^4+1). - _Colin Barker_, Nov 12 2013

%F a(n) = 178*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 11 2013

%t Denominator[Convergents[Sqrt[55], 30]] (* _Vincenzo Librandi_, Dec 11 2013 *)

%t LinearRecurrence[{0,0,0,178,0,0,0,-1},{1,2,5,12,173,358,889,2136},30] (* _Harvey P. Dale_, Nov 24 2022 *)

%o (Magma) I:=[1, 2, 5, 12, 173, 358, 889, 2136]; [n le 8 select I[n] else 178*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 11 2013

%Y Cf. A041094, A010141, A010508, A020812.

%K nonn,cofr,easy,frac

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 12 2013