A040380 Continued fraction for sqrt(401).

20, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40

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 15 2024: (Start)

a(n) = 40 for n >= 1.

G.f.: 20*(1+x)/(1-x).

E.g.f.: 40*exp(x) - 20.

a(n) = 20*A040000(n) = 10*A040002(n) = 5*A040012(n). (End)

Example

20 + 1/(40 + 1/(40 + 1/(40 + 1/(40 + ...)))) = sqrt(401).

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(401)), confrac);

Crossrefs

Cf. A041760/A041761 (convergents).

Cf. A040000, A040002, A040012.

Sequence in context: A215144 A352108 A333234 * A154044 A235289 A296764

Adjacent sequences: A040377 A040378 A040379 * A040381 A040382 A040383

Keyword

nonn,cofr,easy,less

Author

N. J. A. Sloane

Status

approved