A040306 Continued fraction for sqrt(325).

18, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			18 + 1/(36 + 1/(36 + 1/(36 + 1/(36 + ...)))) = sqrt(325).
		

Links

• Index entries for continued fractions for constants
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A041612/A041613 (convergents).

Cf. A040000, A040002, A040006.

Programs

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(325)),confrac);

Mathematica

Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[325],100]] (* or *) PadRight[{18},100,{36}] (* Harvey P. Dale, Dec 01 2020 *)

Formula

From Elmo R. Oliveira, Feb 14 2024: (Start)

a(n) = 36 for n >= 1.

G.f.: 18*(1+x)/(1-x).

E.g.f.: 36*exp(x) - 18.

a(n) = 18*A040000(n) = 9*A040002(n) = 6*A040006(n). (End)