%I #19 Feb 15 2024 17:28:26
%S 24,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,
%T 48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,
%U 48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48
%N Continued fraction for sqrt(577).
%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) = 48 for n >= 1.
%F G.f.: 24*(1+x)/(1-x).
%F E.g.f.: 48*exp(x) - 24.
%F a(n) = 24*A040000(n) = 12*A040002(n) = 8*A040006(n). (End)
%e 24 + 1/(48 + 1/(48 + 1/(48 + 1/(48 + ...)))) = sqrt(577).
%p with(numtheory): Digits := 300: convert(evalf(sqrt(577)),confrac);
%Y Cf. A042104/A042105 (convergents).
%Y Cf. A040000, A040002, A040006.
%K nonn,cofr,easy,less
%O 0,1
%A _N. J. A. Sloane_