%I #19 Feb 15 2024 13:01:59
%S 20,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,
%T 40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,
%U 40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40
%N Continued fraction for sqrt(401).
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F From _Elmo R. Oliveira_, Feb 15 2024: (Start)
%F a(n) = 40 for n >= 1.
%F G.f.: 20*(1+x)/(1-x).
%F E.g.f.: 40*exp(x) - 20.
%F a(n) = 20*A040000(n) = 10*A040002(n) = 5*A040012(n). (End)
%e 20 + 1/(40 + 1/(40 + 1/(40 + 1/(40 + ...)))) = sqrt(401).
%p with(numtheory): Digits := 300: convert(evalf(sqrt(401)),confrac);
%Y Cf. A041760/A041761 (convergents).
%Y Cf. A040000, A040002, A040012.
%K nonn,cofr,easy,less
%O 0,1
%A _N. J. A. Sloane_