The sequence Is satisfied by the sequence if .

Yes, as can be verified by substitution. But there could be other types of sequences that satisfy the recurrence relation. For example,

3, 6, 12, 24, 48, ...

0, 0, 0, 0, 0, 0, ...

But your sequence 1, 0, 0, 0, ... doesn't satisfy the recurrence relation . Do you see why?

- Hollywood