"This Program runs some tests for taus of the form: tau = \
(m+Sqrt[m^2+4l])/2 where l,m. are integers  The first part generates a \
specific tau and some of its powers.  The next part finds the length of the \
repeating block  given a certain m, for all l<m.  The point of this is to \
verify that the expansions for the cases in which l divides m is \
well-determined, wheareas if l is not a factor of m, we the behaviour of the \
expansion is erratic."

<< NumberTheory`ContinuedFractions`

m = 6;  l = 4;  k = 3;
G = Array[g, 200];
g[0] = 0;  g[1] = 1;
For[i = 2, i < 201, i++, 
      g[i] = m*g[i - 1] + l*g[i - 2]]
Array[g, 15]
ContinuedFraction[((m + Sqrt[m^2 + 4  l])/2)^
        k]
b = (g[k + 1] + l*g[k - 1]);
ContinuedFraction[((b + Sqrt[b^2 + 4*(l^k)])/
          2)]

m = 180;
For[l = 1, 
        l < 181, l++, 
Print["l=",  l, "    ", 
            d = ContinuedFraction[(m + Sqrt[m^2 + 4  l])/
                  2]]
   Print["     ",  
            LeafCount[d] - 
              2, " digits in repeating block"]];