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%I #21 Feb 13 2024 08:16:31
%S 12,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,
%T 24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,
%U 24,24,24,24,24,24,24,24
%N Continued fraction for sqrt(145).
%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 12 2024: (Start)
%F a(n) = 24 for n >= 1.
%F G.f.: 12*(1+x)/(1-x).
%F E.g.f.: 24*exp(x) - 12.
%F a(n) = 12*A040000(n) = 6*A040002(n) = 4*A040006(n). (End)
%e 12 + 1/(24 + 1/(24 + 1/(24 + 1/(24 + ...)))) = sqrt(145).
%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t ContinuedFraction[Sqrt[145],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 13 2011*)
%Y Cf. A041264/A041265 (convergents), A176910 (decimal expansion).
%Y Cf. A040000, A040002, A040006.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_.
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