A041787 - OEIS

%I #21 Sep 27 2024 13:13:19

%S 1,2,3,23,49,366,415,1196,48255,97706,145961,1119433,2384827,17813222,

%T 20198049,58209320,2348570849,4755351018,7103921867,54482804087,

%U 116069530041,866969514374,983039044415,2833047603204,114304943172575,231442933948354

%N Denominators of continued fraction convergents to sqrt(414).

%H Vincenzo Librandi, <a href="/A041787/b041787.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, 48670, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^14 -2*x^13 +3*x^12 -23*x^11 +49*x^10 -366*x^9 +415*x^8 -1196*x^7 -415*x^6 -366*x^5 -49*x^4 -23*x^3 -3*x^2 -2*x -1) / (x^16 -48670*x^8 +1). - _Colin Barker_, Nov 24 2013

%F a(n) = 48670*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 24 2013

%t Denominator[Convergents[Sqrt[414], 30]] (* _Vincenzo Librandi_, Dec 24 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,48670,0,0,0,0,0,0,0,-1},{1,2,3,23,49,366,415,1196,48255,97706,145961,1119433,2384827,17813222,20198049,58209320},30] (* _Harvey P. Dale_, Sep 27 2024 *)

%o (Magma) I:=[1,2,3,23,49,366,415,1196,48255,97706,145961, 1119433,2384827,17813222,20198049,58209320]; [n le 16 select I[n] else 48670*Self(n-8)-Self(n-16): n in [1..50]]; // _Vincenzo Librandi_, Dec 24 2013

%Y Cf. A041786, A040393.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 24 2013