A040210 Continued fraction for sqrt(226).

15, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			15 + 1/(30 + 1/(30 + 1/(30 + 1/(30 + ...)))) = sqrt(226).
		

Links

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

Crossrefs

Cf. A041420/A041421 (convergents).

Cf. A040000, A040006, A040020.

Programs

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(226)),confrac);

Formula

From Elmo R. Oliveira, Feb 13 2024: (Start)

a(n) = 30 for n >= 1.

G.f.: 15*(1+x)/(1-x).

E.g.f.: 30*exp(x) - 15.

a(n) = 15*A040000(n) = 5*A040006(n) = 3*A040020(n). (End)