|
%I #16 Sep 08 2022 08:44:54
%S 1,1,2,11,13,76,89,165,3059,3224,6283,34639,40922,239249,280171,
%T 519420,9629731,10149151,19778882,109043561,128822443,753155776,
%U 881978219,1635133995,30314390129,31949524124,62263914253,343269095389,405533009642,2370934143599
%N Denominators of continued fraction convergents to sqrt(91).
%H Vincenzo Librandi, <a href="/A041163/b041163.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 (0,0,0,0,0,0,0,3148,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^14 -x^13 +2*x^12 -11*x^11 +13*x^10 -76*x^9 +89*x^8 -165*x^7 -89*x^6 -76*x^5 -13*x^4 -11*x^3 -2*x^2 -x -1) / (x^16 -3148*x^8 +1). - _Colin Barker_, Nov 14 2013
%F a(n) = 3148*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 12 2013
%t Denominator[Convergents[Sqrt[91], 30]] (* _Bruno Berselli_, Nov 14 2013 *)
%t CoefficientList[Series[-(x^14 - x^13 + 2 x^12 - 11 x^11 + 13 x^10 - 76 x^9 + 89 x^8 - 165 x^7 - 89 x^6 - 76 x^5 - 13 x^4 - 11 x^3 - 2 x^2 - x - 1)/(x^16 - 3148 x^8 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 12 2013 *)
%o (Magma) I:=[1, 1, 2, 11, 13, 76, 89, 165, 3059, 3224, 6283, 34639, 40922, 239249, 280171, 519420]; [n le 16 select I[n] else 3148*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 12 2013
%Y Cf. A041162, A010162, A020848, A010542.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 14 2013
|
