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%I
%S 7,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,
%T 14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,7,14,
%U 7,14,7,14,7,14,7,14,7,14,7
%N Continued fraction for sqrt(51).
%H Harry J. Smith, <a href="/A040043/b040043.txt">Table of n, a(n) for n=0,...,20000</a>
%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%F a(n)=(1/2)*[21+7*(-1)^n]-7*[C(2*n,n) mod 2], with n>=0 [From _Paolo P. Lava_, Jun 09 2009]
%e 7.1414284285428499979993998... = 7 + 1/(7 + 1/(14 + 1/(7 + 1/(14 + ...)))) [From _Harry J. Smith_, Jun 06 2009]
%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t ContinuedFraction[Sqrt[51],300] (*From Vladimir Joseph Stephan Orlovsky, Mar 07 2011*)
%o (PARI) { allocatemem(932245000); default(realprecision, 41000); x=contfrac(sqrt(51)); for (n=0, 20000, write("b040043.txt", n, " ", x[n+1])); } [From _Harry J. Smith_, Jun 06 2009]
%Y Cf. A010504 Decimal expansion. [From _Harry J. Smith_, Jun 06 2009]
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_.
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