|
%I #19 Sep 08 2022 08:44:55
%S 29,30,209,448,6481,13410,86941,100351,5907299,6007650,41953199,
%T 89914048,1300749871,2691413790,17449232611,20140646401,1185606723869,
%U 1205747370270,8420090945489,18045929261248
%N Numerators of continued fraction convergents to sqrt(892).
%H Vincenzo Librandi, <a href="/A042724/b042724.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 200702, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (29 +30*x +209*x^2 +448*x^3 +6481*x^4 +13410*x^5 +86941*x^6 +100351*x^7 +86941*x^8 -13410*x^9 +6481*x^10 -448*x^11 +209*x^12 -30*x^13 +29*x^14 -x^15)/(1 -200702*x^8 +x^16). - _Vincenzo Librandi_, Dec 02 2013
%F a(n) = 200702*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 02 2013
%t Numerator[Convergents[Sqrt[892], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 209 x^2 + 448 x^3 + 6481 x^4 + 13410 x^5 + 86941 x^6 + 100351 x^7 + 86941 x^8 - 13410 x^9 + 6481 x^10 - 448 x^11 + 209 x^12 - 30 x^13 + 29 x^14 - x^15)/(1 - 200702 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 02 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,0,200702,0,0,0,0,0,0,0,-1},{29,30,209,448,6481,13410,86941,100351,5907299,6007650,41953199,89914048,1300749871,2691413790,17449232611,20140646401},20] (* _Harvey P. Dale_, Jul 25 2016 *)
%o (Magma) I:=[29,30,209,448,6481,13410,86941,100351,5907299,6007650,41953199, 89914048,1300749871,2691413790,17449232611,20140646401]; [n le 16 select I[n] else 200702*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 02 2013
%Y Cf. A042725.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
|
