A040132 Continued fraction for sqrt(145).

12, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			12 + 1/(24 + 1/(24 + 1/(24 + 1/(24 + ...)))) = sqrt(145).
		

Links

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

Crossrefs

Cf. A041264/A041265 (convergents), A176910 (decimal expansion).

Cf. A040000, A040002, A040006.

Programs

Maple

Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

Mathematica

ContinuedFraction[Sqrt[145],300] (* Vladimir Joseph Stephan Orlovsky, Mar 13 2011*)

Formula

From Elmo R. Oliveira, Feb 12 2024: (Start)

a(n) = 24 for n >= 1.

G.f.: 12*(1+x)/(1-x).

E.g.f.: 24*exp(x) - 12.

a(n) = 12*A040000(n) = 6*A040002(n) = 4*A040006(n). (End)