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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- Apr 23rd 2011, 10:52 PMOilerRecurrence 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 - Apr 24th 2011, 04:12 AMPlato
Let $\displaystyle S_n$ be the number of stings of length n not containing the pattern 666.

Now it is clear that http://quicklatex.com/cache3/ql_a0ab...2bc70c6_l3.png WHY?

How many of those 999 in $\displaystyle S_3$ end in 66?

So how many are there is $\displaystyle S_4$?

Now find a general pattern.