superprismatic Posted November 17, 2011 Report Share Posted November 17, 2011 How many N-long binary strings are there which don't contain consecutive ones? Quote Link to comment Share on other sites More sharing options...
0 CaptainEd Posted November 17, 2011 Report Share Posted November 17, 2011 If we number the Fibonacci sequence: F(0) = 0, F(1) = 1, sequence is 0,1,1,2,3,5,8,... call S(n) the Superprismatic count--number of binary strings without consecutive 1's. S(n) = F(n+2) When generating the strings of length n, you can prefix any n-1 string with "0", and any n-2 string with "10" and there aren't any others. (The n-2 strings prefixed with "00" are already taken care of) What a cute problem! Thank you, Superprismatic! Quote Link to comment Share on other sites More sharing options...
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superprismatic
How many N-long binary strings are there which don't contain consecutive ones?
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