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

0,1

Links

Table of n, a(n) for n=0..74.

Index entries for continued fractions for constants.

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

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)

Maple

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A040503 A040504 A229555 * A040478 A040477 A040476

Adjacent sequences: A040502 A040503 A040504 * A040506 A040507 A040508

Keyword

nonn,cofr,easy,less,mult

Author

N. J. A. Sloane

Status

approved