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%I A040756 #21 Feb 16 2024 11:27:43
%S A040756 28,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,
%T A040756 56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,
%U A040756 56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56,56
%N A040756 Continued fraction for sqrt(785).
%H A040756 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040756 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A040756 From _Elmo R. Oliveira_, Feb 16 2024: (Start)
%F A040756 a(n) = 56 for n >= 1.
%F A040756 G.f.: 28*(1+x)/(1-x).
%F A040756 E.g.f.: 56*exp(x) - 28.
%F A040756 a(n) = 28*A040000(n) = 14*A040002(n) = 7*A040012(n). (End)
%e A040756 28 + 1/(56 + 1/(56 + 1/(56 + 1/(56 + ...)))) = sqrt(785).
%p A040756 with(numtheory): Digits := 300: convert(evalf(sqrt(785)),confrac);
%t A040756 Block[{$MaxExtraPrecision =1000},ContinuedFraction[Sqrt[785],70]] (* or *) PadRight[{28},70,56] (* _Harvey P. Dale_, May 09 2012 *)
%Y A040756 Cf. A042512/A042513 (convergents).
%Y A040756 Cf. A040000, A040002, A040012.
%K A040756 nonn,cofr,easy
%O A040756 0,1
%A A040756 _N. J. A. Sloane_

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