Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #16 Sep 08 2022 08:44:54
%S 11,12,275,287,6589,6876,157861,164737,3782075,3946812,90611939,
%T 94558751,2170904461,2265463212,52011095125,54276558337,1246095378539,
%U 1300371936876,29854277989811,31154649926687
%N Numerators of continued fraction convergents to sqrt(143).
%H Vincenzo Librandi, <a href="/A041262/b041262.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 (0,24,0,-1).
%F G.f.: (11+12*x+11*x^2-x^3)/(1-24*x^2+x^4). - _Vincenzo Librandi_, Nov 01 2013
%F a(n) = 24*a(n-2)-a(n-4). - _Vincenzo Librandi_, Nov 01 2013
%t Numerator[Convergents[Sqrt[143], 30]] (* or *) CoefficientList[Series[(11 + 12 x + 11 x^2 - x^3)/(1 - 24 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 31 2013 *)
%o (Magma) I:=[11,12,275,287]; [n le 4 select I[n] else 24*Self(n-2)-Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Nov 01 2013
%Y Cf. A041263.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.