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 A040043 Continued fraction for sqrt(51). 4

%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 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1).

%F a(n) = (1/2)*(21 + 7*(-1)^n) - 7*(binomial(2*n,n) mod 2), with n>=0. - _Paolo P. Lava_, Jun 09 2009

%e 7.1414284285428499979993998... = 7 + 1/(7 + 1/(14 + 1/(7 + 1/(14 + ...)))). - _Harry J. Smith_, Jun 06 2009

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

%t ContinuedFraction[Sqrt[51],300] (* _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])); } \\ _Harry J. Smith_, Jun 06 2009

%Y Cf. A010504 Decimal expansion. - _Harry J. Smith_, Jun 06 2009

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_

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