%I #20 Sep 08 2022 08:44:54
%S 1,1,7,15,97,112,3233,3345,23303,49951,323009,372960,10765889,
%T 11138849,77598983,166336815,1075619873,1241956688,35850407137,
%U 37092363825,258404590087,553901543999,3581813854081,4135715398080,119381845000321,123517560398401
%N Denominators of continued fraction convergents to sqrt(221).
%H Vincenzo Librandi, <a href="/A041413/b041413.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 (0,0,0,0,0,3330,0,0,0,0,0,-1).
%F G.f.: -(x^10 -x^9 +7*x^8 -15*x^7 +97*x^6 -112*x^5 -97*x^4 -15*x^3 -7*x^2 -x -1) / ((x^4 -15*x^2 +1)*(x^8 +15*x^6 +224*x^4 +15*x^2 +1)). - _Colin Barker_, Nov 17 2013
%F a(n) = 3330*a(n-6) - a(n-12). - _Vincenzo Librandi_, Dec 17 2013
%t Denominator/@Convergents[Sqrt[221],30] (* _Harvey P. Dale_, Apr 02 2011 *)
%t CoefficientList[Series[-(x^10 - x^9 + 7 x^8 - 15 x^7 + 97 x^6 - 112 x^5 - 97 x^4 - 15 x^3 - 7 x^2 - x - 1)/((x^4 - 15 x^2 + 1) (x^8 + 15 x^6 + 224 x^4 + 15 x^2 + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 17 2013 *)
%o (Magma) I:=[1,1,7,15,97,112,3233,3345,23303,49951,323009, 372960]; [n le 12 select I[n] else 3330*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 17 2013
%Y Cf. A041412, A040206, A177157.
%K nonn,cofr,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 17 2013