A041412 - OEIS

%I #16 Jul 13 2024 15:36:01

%S 14,15,104,223,1442,1665,48062,49727,346424,742575,4801874,5544449,

%T 160046446,165590895,1153591816,2472774527,15990238978,18463013505,

%U 532954617118,551417630623,3841460400856,8234338432335,53247490994866,61481829427201,1774738714956494

%N Numerators of continued fraction convergents to sqrt(221).

%H Vincenzo Librandi, <a href="/A041412/b041412.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,3330,0,0,0,0,0,-1).

%F G.f.: -(x^11 -14*x^10 +15*x^9 -104*x^8 +223*x^7 -1442*x^6 -1665*x^5 -1442*x^4 -223*x^3 -104*x^2 -15*x -14) / ((x^4 -15*x^2 +1)*(x^8 +15*x^6 +224*x^4 +15*x^2 +1)). - _Colin Barker_, Nov 07 2013

%F a(n) = 3330*a(n-6)-a(n-12). - _Wesley Ivan Hurt_, May 24 2021

%t Numerator[Convergents[Sqrt[221], 30]] (* _Vincenzo Librandi_, Nov 01 2013 *)

%t LinearRecurrence[{0,0,0,0,0,3330,0,0,0,0,0,-1},{14,15,104,223,1442,1665,48062,49727,346424,742575,4801874,5544449},30] (* _Harvey P. Dale_, Jul 13 2024 *)

%Y Cf. A041413.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 07 2013