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A010174 Continued fraction for sqrt(108). 3
10, 2, 1, 1, 4, 1, 1, 2, 20, 2, 1, 1, 4, 1, 1, 2, 20, 2, 1, 1, 4, 1, 1, 2, 20, 2, 1, 1, 4, 1, 1, 2, 20, 2, 1, 1, 4, 1, 1, 2, 20, 2, 1, 1, 4, 1, 1, 2, 20, 2, 1, 1, 4, 1, 1, 2, 20, 2, 1, 1, 4, 1, 1, 2, 20, 2, 1, 1, 4, 1, 1, 2, 20, 2, 1, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..999

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)*{-118*(n mod 8)+[(n+1) mod 8]+8*[(n+2) mod 8]+29*[(n+3) mod 8]-13*[(n+4) mod 8]+8*[(n+5) mod 8]+15*[(n+6) mod 8]+134*[(n+7) mod 8]}-10*[C(2*n,n) mod 2], with n>=0. [Paolo P. Lava, Jul 24 2009]

G.f.: (10+2*x+x^2+x^3+4*x^4+x^5+x^6+2*x^7+10*x^8) / (1-x^8). - Wesley Ivan Hurt, Apr 22 2016

MAPLE

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

MATHEMATICA

ContinuedFraction[Sqrt[108], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2011*)

CoefficientList[Series[(10 + 2 x + x^2 + x^3 + 4 x^4 + x^5 + x^6 + 2 x^7 + 10 x^8)/(1 - x^8), {x, 0, 100}], x] (* Wesley Ivan Hurt, Apr 22 2016 *)

CROSSREFS

Sequence in context: A261942 A057603 A040097 * A073755 A010173 A259712

Adjacent sequences:  A010171 A010172 A010173 * A010175 A010176 A010177

KEYWORD

nonn,cofr

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.