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Denominators of continued fraction convergents to sqrt(770).
2

%I #13 Sep 08 2022 08:44:55

%S 1,1,3,4,219,223,665,888,48617,49505,147627,197132,10792755,10989887,

%T 32772529,43762416,2395942993,2439705409,7275353811,9715059220,

%U 531888551691,541603610911,1615095773513,2156699384424,118076862532409,120233561916833,358543986366075

%N Denominators of continued fraction convergents to sqrt(770).

%H Vincenzo Librandi, <a href="/A042485/b042485.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 (0,0,0,222,0,0,0,-1).

%F G.f.: -(x^2 -x -1)*(x^4 +4*x^2 +1) / (x^8 -222*x^4 +1). - _Colin Barker_, Dec 15 2013

%F a(n) = 222*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 15 2013

%t Denominator[Convergents[Sqrt[770], 30]] (* _Vincenzo Librandi_, Dec 15 2013 *)

%o (Magma) I:=[1,1,3,4,219,223,665,888]; [n le 8 select I[n] else 222*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 15 2013

%Y Cf. A042484, A040742.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 15 2013