"This Program prints out the continued fraction expansions of the \
k-neighbour ratios of the i^th fibonacci terms, for k = 3,4,...,9 and for i = \
20,...,100"

<< NumberTheory`ContinuedFractions`

For[i = 20, i < 100, i++, 
      Print["i=",  i   , "        ",  
        d = ContinuedFraction[Fibonacci[i]/Fibonacci[i - 3]]]]

For[i = 20, i < 100, i++, 
      Print["i=",  i   , "        ",  
        d = ContinuedFraction[Fibonacci[i]/Fibonacci[i - 4]]]]

For[i = 20, i < 100, i++, 
      Print["i=",  i   , "        ",  
        d = ContinuedFraction[Fibonacci[i]/Fibonacci[i - 5]]]]

For[i = 20, i < 100, i++, 
      Print["i=",  i   , "        ",  
        d = ContinuedFraction[Fibonacci[i]/Fibonacci[i - 6]]]]

For[i = 20, i < 100, i++, 
      Print["i=",  i   , "        ",  
        d = ContinuedFraction[Fibonacci[i]/Fibonacci[i - 7]]]]

For[i = 20, i < 100, i++, 
      Print["i=",  i   , "        ",  
        d = ContinuedFraction[Fibonacci[i]/Fibonacci[i - 8]]]]

For[i = 20, i < 100, i++, 
      Print["i=",  i   , "        ",  
        d = ContinuedFraction[Fibonacci[i]/Fibonacci[i - 9]]]]