A040505 Continued fraction for sqrt(528).

22, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44, 1, 44

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• less
• mult

Links

• Index entries for continued fractions for constants.
• Index entries for linear recurrences with constant coefficients, signature (0,1).

Programs

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(528)),confrac);

Mathematica

ContinuedFraction[Sqrt[528], 100] (* Amiram Eldar, Dec 26 2023 *)

PARI

Vec(-(22*x^2+x+22)/((x-1)*(x+1)) + O(x^100)) \\ Colin Barker, Nov 10 2014

Formula

From Colin Barker, Nov 10 2014: (Start)

a(n) = (45+43*(-1)^n)/2 for n>0.

a(n) = a(n-2) for n>2.

G.f.: -(22*x^2+x+22) / ((x-1)*(x+1)). (End)

From Amiram Eldar, Dec 26 2023: (Start)

Multiplicative with a(2^e) = 44, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 43/2^s). (End)