- Thread starter
- #1
- Jan 26, 2012
- 644
[JUSTIFY]Just an easy one to start off with, find a non-recursive formula for the $n$th term of the following linear homogeneous recurrence:
$$a_0 = 2, ~ ~ a_1 = -2, ~ ~ a_n = -2 a_{n - 1} + 2 a_{n - 2} ~ ~ \text{for} ~ n \geq 2$$[/JUSTIFY]
[HR][/HR]
Hint:
$$a_0 = 2, ~ ~ a_1 = -2, ~ ~ a_n = -2 a_{n - 1} + 2 a_{n - 2} ~ ~ \text{for} ~ n \geq 2$$[/JUSTIFY]
[HR][/HR]
Hint:
You can use generating functions to solve this problem.