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A040600 Continued fraction for sqrt(626).

%I A040600 #18 Feb 16 2024 05:49:34
%S A040600 25,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,
%T A040600 50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,
%U A040600 50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50
%N A040600 Continued fraction for sqrt(626).
%H A040600 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040600 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A040600 From _Elmo R. Oliveira_, Feb 15 2024: (Start)
%F A040600 a(n) = 50 for >= 1.
%F A040600 G.f.: 25*(1+x)/(1-x).
%F A040600 E.g.f.: 50*exp(x) - 25.
%F A040600 a(n) = 25*A040000(n) = 5*A040020(n). (End)
%e A040600 25 + 1/(50 + 1/(50 + 1/(50 + 1/(50 + ...)))) = sqrt(626).
%p A040600 with(numtheory): Digits := 300: convert(evalf(sqrt(626)),confrac);
%Y A040600 Cf. A042200/A042201 (convergents).
%Y A040600 Cf. A040000, A040020.
%K A040600 nonn,cofr,easy
%O A040600 0,1
%A A040600 _N. J. A. Sloane_