|
%I #20 Jun 26 2022 23:54:34
%S 31,63,94,2883,2977,8837,550871,1110579,1661450,50954079,52615529,
%T 156185137,9736094023,19628373183,29364467206,900562389363,
%U 929926856569,2760416102501,172075725211631,346911866525763,518987591737394,15916539618647583,16435527210384977
%N Numerators of continued fraction convergents to sqrt(982).
%H Vincenzo Librandi, <a href="/A042900/b042900.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, 17674, 0, 0, 0, 0, 0, -1).
%F G.f.: (31 + 63*x + 94*x^2 + 2883*x^3 + 2977*x^4 + 8837*x^5 + 2977*x^6 - 2883*x^7 + 94*x^8 - 63*x^9 + 31*x^10 - x^11)/(1 - 17674*x^6 + x^12). - _Vincenzo Librandi_, Dec 09 2013
%F a(n) = 17674*a(n-6) - a(n-12). - _Vincenzo Librandi_, Dec 09 2013
%t Numerator[Convergents[Sqrt[982], 30]] (* or *) CoefficientList[Series[(31 + 63 x + 94 x^2 + 2883 x^3 + 2977 x^4 + 8837 x^5 + 2977 x^6 - 2883 x^7 + 94 x^8 - 63 x^9 + 31 x^10 - x^11)/(1 - 17674 x^6 + x^12), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 09 2013 *)
%o (Magma) I:=[31,63,94,2883,2977,8837,550871,1110579,1661450,50954079, 52615529,156185137]; [n le 12 select I[n] else 17674*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Dec 09 2013
%Y Cf. A042901.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Dec 09 2013
|
