A040858 Continued fraction for sqrt(888).

29, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1, 58, 1, 3, 1

Offset

0,1

Links

Table of n, a(n) for n=0..83.

Index entries for continued fractions for constants.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Formula

From Wesley Ivan Hurt, Aug 29 2015: (Start)

G.f.: (29+x+3*x^2+x^3+29*x^4)/(1-x^4).

a(n) = 2+(-1)^n+55*((1+(-1)^(n/2))*(1+(-1)^n))/4, n>0. (End)

From Amiram Eldar, Jan 17 2024: (Start)

Multiplicative with a(2) = 3, a(2^e) = 58 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-1) + 55/2^(2*s)). (End)

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(888)), confrac);

Mathematica

CoefficientList[Series[(29 + x + 3 x^2 + x^3 + 29 x^4)/(1 - x^4), {x, 0, 30}], x] (* or *) Join[{29}, Table[2 + (-1)^n + 55 ((1 + (-1)^(n/2))*(1 + (-1)^n))/4, {n, 100}]] (* Wesley Ivan Hurt, Aug 29 2015 *)
ContinuedFraction[Sqrt[888], 100] (* Amiram Eldar, Jan 17 2024 *)

Crossrefs

Sequence in context: A040852 A040851 A040857 * A040856 A040860 A040859

Adjacent sequences: A040855 A040856 A040857 * A040859 A040860 A040861

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved