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%I #21 Feb 16 2024 11:27:43
%S 28,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,
%T 56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,
%U 56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56
%N Continued fraction for sqrt(785).
%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 16 2024: (Start)
%F a(n) = 56 for n >= 1.
%F G.f.: 28*(1+x)/(1-x).
%F E.g.f.: 56*exp(x) - 28.
%F a(n) = 28*A040000(n) = 14*A040002(n) = 7*A040012(n). (End)
%e 28 + 1/(56 + 1/(56 + 1/(56 + 1/(56 + ...)))) = sqrt(785).
%p with(numtheory): Digits := 300: convert(evalf(sqrt(785)),confrac);
%t Block[{$MaxExtraPrecision =1000},ContinuedFraction[Sqrt[785],70]] (* or *) PadRight[{28},70,56] (* _Harvey P. Dale_, May 09 2012 *)
%Y Cf. A042512/A042513 (convergents).
%Y Cf. A040000, A040002, A040012.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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