Recurrence Relation First Five Terms

Recurrence Relation First Five Terms

Currently in my discrete math class we are working on Recurrence Relations and sequences. Now there are similar problems to mine on here but I could not find what I was looking for. My teacher for this class just plain cannot teach and was hoping someone could help explain this to me. The problem I have is to find the first five terms of this sequence: a_n3a_n-1 - 1; with a_1 1 Then I have to find an explicit or closed definition for this sequence If anyone could please offer up some help it would truly be appreciated.

a_23a_131a_1-30 a_333a_1-1-19a_1-432a_1-3031 a_439a_1-4-127a_1-1333a_1-303132 and so forth. Since a_11, we get a_n3n-1-sum_k0n-23k

Constructing the first terms of the sequence as suggested in the comments you can also arrive at a closed expression. As example, from: a_43a_3-133a_2-1-1333a_1-1-1-1333cdot 1-1-1-1332-3-1-133-32-31-1 it is suggested that, for n1, we have: a_n3n-1-sum_k0n-23k and you can verify that this result satisfies the given recursive definition.

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