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Math Help - Recurrence relation

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    Recurrence relation

    Hi,

    how can I find the recurrence relation and its initial conditions for the number of decimal strings of length n that do not contain the string 666. Thanks
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  2. #2
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    Quote Originally Posted by Oiler View Post
    find the recurrence relation and its initial conditions for the number of decimal strings of length n that do not contain the string 666.
    Let S_n be the number of stings of length n not containing the pattern 666.
    Now it is clear that WHY?
    How many of those 999 in S_3 end in 66?
    So how many are there is S_4?
    Now find a general pattern.
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