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%I #18 Feb 16 2024 05:49:34
%S 25,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,
%T 50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,
%U 50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50
%N Continued fraction for sqrt(626).
%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) = 50 for >= 1.
%F G.f.: 25*(1+x)/(1-x).
%F E.g.f.: 50*exp(x) - 25.
%F a(n) = 25*A040000(n) = 5*A040020(n). (End)
%e 25 + 1/(50 + 1/(50 + 1/(50 + 1/(50 + ...)))) = sqrt(626).
%p with(numtheory): Digits := 300: convert(evalf(sqrt(626)),confrac);
%Y Cf. A042200/A042201 (convergents).
%Y Cf. A040000, A040020.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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