%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_