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%I #23 Feb 14 2024 10:46:16
%S 15,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,
%T 30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,
%U 30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30
%N Continued fraction for sqrt(226).
%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 13 2024: (Start)
%F a(n) = 30 for n >= 1.
%F G.f.: 15*(1+x)/(1-x).
%F E.g.f.: 30*exp(x) - 15.
%F a(n) = 15*A040000(n) = 5*A040006(n) = 3*A040020(n). (End)
%e 15 + 1/(30 + 1/(30 + 1/(30 + 1/(30 + ...)))) = sqrt(226).
%p with(numtheory): Digits := 300: convert(evalf(sqrt(226)),confrac);
%Y Cf. A041420/A041421 (convergents).
%Y Cf. A040000, A040006, A040020.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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