|
%I #17 Sep 08 2022 08:44:55
%S 1,2,5,7,201,208,617,1442,84253,169948,424149,594097,17058865,
%T 17652962,52364789,122382540,7150552109,14423486758,35997525625,
%U 50421012383,1447785872349,1498206884732,4444199641813,10386606168358,606867357406577,1224121320981512
%N Denominators of continued fraction convergents to sqrt(866).
%H Vincenzo Librandi, <a href="/A042673/b042673.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 84870, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^14 -2*x^13 +5*x^12 -7*x^11 +201*x^10 -208*x^9 +617*x^8 -1442*x^7 -617*x^6 -208*x^5 -201*x^4 -7*x^3 -5*x^2 -2*x -1) / (x^16 -84870*x^8 +1). - _Colin Barker_, Dec 20 2013
%F a(n) = 84870*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 20 2013
%t Denominator[Convergents[Sqrt[866], 30]] (* _Vincenzo Librandi_, Dec 20 2013 *)
%o (Magma) I:=[1,2,5,7,201,208,617,1442,84253,169948, 424149,594097,17058865,17652962,52364789,122382540]; [n le 16 select I[n] else 84870*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2013
%Y Cf. A042672, A040836.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Dec 20 2013
|
