THX For each integer n Greaterthanorequalto 1 let tn be the

THX

For each integer n Greaterthanorequalto 1, let t_n be the number of strings of n letters that can be produced by concatenating (running together) copies of the strings \"a\", \"6c\" and \"c6\". For example, 11 = 1 (\"a\" is the only possible string) and to = 3 (\"act\", \"6c\" and \"c\" are the possible strings). Find t_j and 14. Find a recurrence for t_n that holds for all n Greaterthanorequalto 3. Explain why your recurrence gives t_n.

Solution

In this method, we draw a recurrence tree and calculate the time taken by every level of tree. Finally, we sum the work done at all levels. To draw the recurrence tree, we start from the given recurrence and keep drawing till we find a pattern among levels. The pattern is typically a arithmetic or geometric series.