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A040037 Continued fraction for sqrt(44). 3
6, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. Xiao, Contfrac

Index entries for continued fractions for constants

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

FORMULA

a(n) = (1/56)*{-72*(n mod 8) + 5*((n+1) mod 8) + 5*((n+2) mod 8) + 12*((n+3) mod 8) - 2*((n+4) mod 8) + 5*((n+5) mod 8) + 5*((n+6) mod 8) + 82*((n+7) mod 8)) - 6*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 09 2009

EXAMPLE

6.633249580710799698229865473... = 6 + 1/(1 + 1/(1 + 1/(1 + 1/(2 + ...)))). - Harry J. Smith, Jun 05 2009

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[44], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

PadRight[{6}, 80, {12, 1, 1, 1, 2, 1, 1, 1}] (* Harvey P. Dale, Apr 02 2013 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 14000); x=contfrac(sqrt(44)); for (n=0, 20000, write("b040037.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009

CROSSREFS

Cf. A010498 Decimal expansion. - Harry J. Smith, Jun 05 2009

Sequence in context: A268731 A080219 A293901 * A009194 A007732 A237835

Adjacent sequences:  A040034 A040035 A040036 * A040038 A040039 A040040

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 20 18:26 EDT 2018. Contains 315240 sequences. (Running on oeis4.)