login
Numerators of continued fraction convergents to sqrt(678).
2

%I #15 Sep 08 2022 08:44:55

%S 26,677,35230,916657,47701394,1241152901,64587652246,1680520111297,

%T 87451633439690,2275422989543237,118409447089688014,

%U 3080921047321431601,160326303907804131266,4171564822650228844517,217081697081719704046150

%N Numerators of continued fraction convergents to sqrt(678).

%H Vincenzo Librandi, <a href="/A042302/b042302.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 (0,1354,0,-1).

%F G.f.: (26 +677*x +26*x^2 -x^3)/(1 -1354*x^2 +x^4). - _Vincenzo Librandi_, Nov 21 2013

%F a(n) = 1354*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 21 2013

%t Numerator[Convergents[Sqrt[678], 20]] (* _Harvey P. Dale_, Oct 08 2012 *)

%t CoefficientList[Series[(26 + 677 x + 26 x^2 - x^3)/(1 - 1354 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 21 2013 *)

%o (Magma) I:=[26, 677, 35230, 916657]; [n le 4 select I[n] else 1354*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 21 2013

%Y Cf. A042303.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.