A041779 - OEIS

%I #25 Sep 08 2022 08:44:54

%S 1,4,161,648,26081,104972,4224961,17004816,684417601,2754675220,

%T 110871426401,446240380824,17960486659361,72288187018268,

%U 2909487967390081,11710240056578592,471319090230533761,1896986600978713636,76350783129379079201

%N Denominators of continued fraction convergents to sqrt(410).

%H Vincenzo Librandi, <a href="/A041779/b041779.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 162, 0, -1).

%F a(n) = 162*a(n-2)-a(n-4). G.f.: -(x^2-4*x-1)/(x^4-162*x^2+1). [_Colin Barker_, Jul 16 2012]

%t Denominator[Convergents[Sqrt[410], 30]] (* _Harvey P. Dale_, Nov 06 2011 *)

%t CoefficientList[Series[(1 + 4 x - x^2)/(x^4 - 162 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 24 2013 *)

%o (Magma) I:=[1,4,161,648]; [n le 4 select I[n] else 162*Self(n-2)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Dec 24 2013

%Y Cf. A041778.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 24 2013