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%I #31 Feb 14 2024 10:46:12
%S 14,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
%T 28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
%U 28,28,28,28,28,28,28,28,28,28
%N Continued fraction for sqrt(197).
%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) = 28 for n >= 1.
%F G.f.: 14*(1+x)/(1-x).
%F E.g.f.: 28*exp(x) - 14.
%F a(n) = 14*A040000(n) = 7*A040002(n) = 2*A040042(n). (End)
%e 14 + 1/(28 + 1/(28 + 1/(28 + 1/(28 + ...)))) = sqrt(197).
%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t ContinuedFraction[Sqrt[197],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 28 2011 *)
%t PadRight[{14},120,{28}] (* _Harvey P. Dale_, May 02 2022 *)
%Y Cf. A041364/A041365 (convergents).
%Y Cf. A040000, A040002, A040042.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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