%I #18 Feb 16 2024 05:50:02
%S 27,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,
%T 54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,
%U 54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54
%N Continued fraction for sqrt(730).
%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) = 54 for n >= 1.
%F G.f.: 27*(1+x)/(1-x).
%F E.g.f.: 54*exp(x) - 27.
%F a(n) = 27*A040000(n) = 9*A040006(n) = 3*A040072(n). (End)
%e 27 + 1/(54 + 1/(54 + 1/(54 + 1/(54 + ...)))) = sqrt(730).
%p with(numtheory): Digits := 300: convert(evalf(sqrt(730)),confrac);
%Y Cf. A042404/A042405 (convergents).
%Y Cf. A040000, A040006, A040072.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_