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Denominators of continued fraction convergents to sqrt(95).
2

%I #19 Sep 08 2022 08:44:54

%S 1,1,3,4,75,79,233,312,5849,6161,18171,24332,456147,480479,1417105,

%T 1897584,35573617,37471201,110516019,147987220,2774285979,2922273199,

%U 8618832377,11541105576,216358732745,227899838321,672158409387,900058247708,16873206868131,17773265115839

%N Denominators of continued fraction convergents to sqrt(95).

%H Vincenzo Librandi, <a href="/A041171/b041171.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 (0,0,0,78,0,0,0,-1).

%F G.f.: (1 +x +3*x^2 +4*x^3 -3*x^4 +x^5 -x^6)/(1 -78*x^4 +x^8). - _Vincenzo Librandi_, Dec 12 2013

%F a(n) = 78*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 12 2013

%t Denominator[Convergents[Sqrt[95], 30]] (* or *) CoefficientList[Series[(1 + x + 3 x^2 + 4 x^3 - 3 x^4 + x^5 - x^6)/(1 - 78 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 12 2013 *)

%t LinearRecurrence[{0,0,0,78,0,0,0,-1},{1,1,3,4,75,79,233,312},30] (* _Harvey P. Dale_, Mar 12 2016 *)

%o (Magma) I:=[1, 1, 3, 4, 75, 79, 233, 312]; [n le 8 select I[n] else 78*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 12 2013

%Y Cf. A041170.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 12 2013