A041409 - OEIS

%I #18 Sep 08 2022 08:44:54

%S 1,1,4,5,144,149,591,740,21311,22051,87464,109515,3153884,3263399,

%T 12944081,16207480,466753521,482961001,1915636524,2398597525,

%U 69076367224,71474964749,283501261471,354976226220,10222835595631,10577811821851,41956271061184

%N Denominators of continued fraction convergents to sqrt(219).

%H Vincenzo Librandi, <a href="/A041409/b041409.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 (0,0,0,148,0,0,0,-1).

%F G.f.: -(x^2-x-1)*(x^4+5*x^2+1) / (x^8-148*x^4+1). - _Colin Barker_, Nov 17 2013

%F a(n) = 148*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Dec 17 2013

%t Denominator[Convergents[Sqrt[219], 30]] (* _Vincenzo Librandi_, Dec 17 2013 *)

%o (Magma) I:=[1,1,4,5,144,149,591,740]; [n le 8 select I[n] else 148*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 17 2013

%Y Cf. A041408, A040204.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 17 2013