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

0,1

Links

Table of n, a(n) for n=0..62.

Index entries for continued fractions for constants

Index entries for linear recurrences with constant coefficients, signature (1).

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)

Example

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

Maple

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

Crossrefs

Cf. A041420/A041421 (convergents).

Cf. A040000, A040006, A040020.

Sequence in context: A201136 A200896 A322370 * A296758 A297285 A115776

Adjacent sequences: A040207 A040208 A040209 * A040211 A040212 A040213

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved